View source for User:Ulf Rehmann/Table of automatically generated TeX code

==[[Algebraic curve]]==
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| 1.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|23.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011450/a01145065.png || $g \leq \left\{ \begin{array} { l l } { \frac { ( n - 2 ) ^ { 2 } } { 4 } } & { \text { for even } n } \\ { \frac { ( n - 1 ) ( n - 3 ) } { 4 } } & { \text { for odd } n } \end{array} \right.$ ||  $$ g \leq \left\{ \begin{array} { l l } { \frac { ( n - 2 ) ^ { 2 } } { 4 } } & { \text { for even } n, } \\ { \frac { ( n - 1 ) ( n - 3 ) } { 4 } } & { \text { for odd } n, } \end{array} \right.$$  || conf 0.698
 
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==[[Algebraic geometry]]==
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| 2.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|116.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150014.png || $\theta = \int _ { 0 } ^ { \lambda } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ||  $$\theta = \int\limits _ { 0 } ^ { \lambda } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }, $$ || conf 0.997
 
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| 3.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|133.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150021.png || $\omega = 2 \int _ { 0 } ^ { 1 / c } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ ||  $$\omega = 2 \int\limits _ { 0 } ^ { 1 / c } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }, $$ || conf 0.973
 
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| 4.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|67.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150022.png || $\overline { w } = 2 \int _ { 0 } ^ { 1 / \varepsilon } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } }$ || $$\widetilde{ w } = 2 \int\limits _ { 0 } ^ { 1 / \varepsilon } \frac { d x } { \sqrt { ( 1 - c ^ { 2 } x ^ { 2 } ) ( 1 - e ^ { 2 } x ^ { 2 } ) } },$$ || conf 0.107 
 
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| 5.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|105.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150044.png || $\theta ( v + \pi i r ) = \theta ( r ) , \quad \theta ( v + \alpha _ { j } ) = e ^ { L _ { j } ( v ) } \theta ( v )$ ||  $$\theta ( v + \pi i r ) = \theta ( r ) , \quad \theta ( v + \alpha _ { j } ) = e ^ { L _ { j } ( v ) } \theta ( v ), $$ || conf 0.775
 
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| 6.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|17.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011500/a01150078.png || $\left( \begin{array} { l l } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \equiv \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) ( \operatorname { mod } 7 )$ ||  $$\left( \begin{array} { l l } { \alpha } & { b } \\ { c } & { d } \end{array} \right) \equiv \left( \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right) ( \operatorname { mod } 7 ). $$ || conf 0.440
 
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==[[Algebraic surface]]==
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| 7.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|144.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640132.png || $0 \rightarrow O _ { V } \rightarrow E _ { \alpha } \rightarrow T _ { V } \rightarrow 0$ || $$0 \rightarrow {\cal O} _ { V } \rightarrow E _ { \alpha } \rightarrow T _ { V } \rightarrow 0$$   || conf 0.981
 
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| 8.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|73.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640137.png  || $M = \operatorname { dim } \operatorname { Im } ( H ^ { 1 } ( V , E _ { \alpha } ) \rightarrow H ^ { 1 } ( V , T _ { V } ) )$ || $$ M = \operatorname { dim } \operatorname { Im } ( H ^ { 1 } ( V , E _ { \alpha } ) \rightarrow H ^ { 1 } ( V , T _ { V } ) ). $$|| conf 0.997
 
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| 9.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|88.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a011640139.png  || $\operatorname { dim } _ { k } H ^ { 2 } ( V , E _ { \alpha } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , T _ { V } )$ || $$ \operatorname { dim } _ { k } H ^ { 2 } ( V , E _ { \alpha } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , T _ { V } ). $$|| conf 0.996
 
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| 10.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|117.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164027.png  || $N _ { m } = \left( \begin{array} { c } { m + 3 } \\ { 3 } \end{array} \right) - d m + 2 t + \tau + p - 1$ || $$ N _ { m } = \left( \begin{array} { c } { m + 3 } \\ { 3 } \end{array} \right) - d m + 2 t + \tau + p - 1. $$|| conf 0.369
 
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| 11.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|72.]]) ||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164029.png  || $p _ { \alpha } ( V ) = \left( \begin{array} { c } { n - 1 } \\ { 3 } \end{array} \right) - d ( n - 1 ) + 2 t + \tau + p - 1$ || $$ p _ { \alpha } ( V ) = \left( \begin{array} { c } { n - 1 } \\ { 3 } \end{array} \right) - d ( n - 1 ) + 2 t + \tau + p - 1 $$|| conf 0.396
 
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| 12.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|68.]])*||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164047.png || $p _ { x } ( V ) = - \operatorname { dim } _ { k } H _ { 1 } ( V , O _ { V } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , O _ { V } ) =$ ||  $$p _ { \alpha } ( V ) = - \operatorname { dim } _ { k } H _ { 1 } ( V , {\cal O} _ { V } ) + \operatorname { dim } _ { k } H ^ { 2 } ( V , {\cal O} _ { V } ) =$$ || conf 0.756  F 
 
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| 13.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|93.]])*||  https://www.encyclopediaofmath.org/legacyimages/a/a011/a011640/a01164053.png || $1 + p _ { x } ( V ) = \frac { \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + \operatorname { deg } ( c _ { 2 } ) } { 12 }$ ||  $$ 1 + p _ { \alpha } ( V ) = \frac { \operatorname { deg } ( c _ { 1 } ^ { 2 } ) + \operatorname { deg } ( c _ { 2 } ) } { 12 },$$|| conf 0.752  F 
 
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==[[Cartan subalgebra]]==
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| 14.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|33.]])*||  https://www.encyclopediaofmath.org/legacyimages/c/c020/c020550/c0205509.png || $\mathfrak { g } 0 = \{ X \in \mathfrak { g } : \forall H \in \mathfrak { t } \exists \mathfrak { n } X , H \in Z ( ( \text { ad } H ) ^ { n } X , H ( X ) = 0 ) \}$ ||  $$\mathfrak { g }_0 = \big\{ X \in \mathfrak { g } : \forall H \in \mathfrak { t } \exists { n }_{X,H} \in {\mathbb Z} ( ( \text { ad } H ) ^ { n_{X , H} } ( X ) = 0 ) \big\},$$ || conf 0.110  F 

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==[[Cartan theorem]]==
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| 15.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|49.]])*||  https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c0205704.png  || $f _ { j } ] = \delta _ { i j } h _ { i } , \quad [ h _ { i } , e _ { j } ] = \alpha _ { i j } e _ { j } , \quad [ h _ { i } , f _ { j } ] = - \alpha _ { j } f _ { j }$ || $$ [e_i, f _ { j } ] = \delta _ { i j } h _ { i } , \quad [ h _ { i } , e _ { j } ] = \alpha _ { i j } e _ { j } , \quad [ h _ { i } , f _ { j } ] = - \alpha _ { ij } f _ { j }, $$|| conf 0.149  F 
 
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| 16.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|55.]])*||  https://www.encyclopediaofmath.org/legacyimages/c/c020/c020570/c02057064.png  || $\rightarrow H ^ { p } ( X , S ) \rightarrow H ^ { p } ( X , F ) \stackrel { \phi p } { \rightarrow } H ^ { p } ( X , G ) \rightarrow$ || $$ \dots \rightarrow H ^ { p } ( X , S ) \rightarrow H ^ { p } ( X , F ) \stackrel { \phi_p } { \rightarrow } H ^ { p } ( X , G ) \rightarrow $$|| conf 0.853  F 
 
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==[[Comitant]]==
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| 17.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|7.]]) ||  https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333033.png || $H = \frac { 1 } { 36 } \left| \begin{array} { c c } { \frac { \partial ^ { 2 } f } { \partial x ^ { 2 } } } & { \frac { \partial ^ { 2 } f } { \partial x \partial y } } \\ { \frac { \partial ^ { 2 } f } { \partial x \partial y } } & { \frac { \partial ^ { 2 } f } { \partial y ^ { 2 } } } \end{array} \right| =$ || $$H = \frac { 1 } { 36 } \left| \begin{array} { c c } { \frac { \partial ^ { 2 } f } { \partial x ^ { 2 } } } & { \frac { \partial ^ { 2 } f } { \partial x \partial y } } \\ { \frac { \partial ^ { 2 } f } { \partial x \partial y } } & { \frac { \partial ^ { 2 } f } { \partial y ^ { 2 } } } \end{array} \right| =$$  || conf 0.956
 
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| 18.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|76.]]) ||  https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333034.png  || $= ( a _ { 0 } a _ { 2 } - a _ { 1 } ^ { 2 } ) x ^ { 2 } + ( a _ { 0 } a _ { 3 } - a _ { 1 } a _ { 2 } ) x y + ( a _ { 1 } a _ { 3 } - a _ { 2 } ^ { 2 } ) y ^ { 2 }$ || $$ = ( a _ { 0 } a _ { 2 } - a _ { 1 } ^ { 2 } ) x ^ { 2 } + ( a _ { 0 } a _ { 3 } - a _ { 1 } a _ { 2 } ) x y + ( a _ { 1 } a _ { 3 } - a _ { 2 } ^ { 2 } ) y ^ { 2 } $$|| conf 0.549
 
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| 19.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|11.]])*||  https://www.encyclopediaofmath.org/legacyimages/c/c023/c023330/c02333035.png  || $( \alpha _ { 0 } , \alpha _ { 1 } , \alpha _ { 2 } , \alpha _ { 3 } ) \mapsto ( \alpha _ { 0 } \alpha _ { 2 } - \alpha _ { 1 } ^ { 2 } , \frac { 1 } { 2 } ( \alpha _ { 0 } \alpha _ { 3 } - \alpha _ { 1 } \alpha _ { 2 } ) , \alpha _ { 1 } \alpha _ { 3 } - \alpha _ { 2 } ^ { 2 } )$ || $$ ( \alpha _ { 0 } , \alpha _ { 1 } , \alpha _ { 2 } , \alpha _ { 3 } ) \mapsto ( \alpha _ { 0 } \alpha _ { 2 } - \alpha _ { 1 } ^ { 2 } , \frac { 1 } { 2 } ( \alpha _ { 0 } \alpha _ { 3 } - \alpha _ { 1 } \alpha _ { 2 } ) , \alpha _ { 1 } \alpha _ { 3 } - \alpha _ { 2 } ^ { 2 } ) $$|| conf 0.521  F 
 
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==[[Deformation]]==
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| 20.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|26.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700175.png || $\operatorname { Aut } _ { R ^ { \prime } } ( X ^ { \prime } | X _ { 0 } ) \rightarrow \operatorname { Aut } _ { R } ( X _ { R ^ { \prime } } ^ { \prime } \otimes R | X _ { 0 } )$ ||  $$ \operatorname { Aut } _ { R ^ { \prime } } ( X ^ { \prime } | X _ { 0 } ) \rightarrow \operatorname { Aut } _ { R } ( X _ { R ^ { \prime } } ^ { \prime } \otimes R | X _ { 0 } )  $$ || conf 0.683
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| 21.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|27.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700190.png  || $\operatorname { dim } _ { k } H ^ { 1 } ( X _ { 0 } , T _ { X _ { 0 } } ) - \operatorname { dim } M _ { X _ { 0 } } \leq \operatorname { dim } _ { k } H ^ { 2 } ( X _ { 0 } , T _ { X _ { 0 } } )$ || $$ \operatorname { dim } _ { k } H ^ { 1 } ( X _ { 0 } , T _ { X _ { 0 } } ) - \operatorname { dim } M _ { X _ { 0 } } \leq \operatorname { dim } _ { k } H ^ { 2 } ( X _ { 0 } , T _ { X _ { 0 } } ). $$|| conf 0.944
 
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| 22.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|78.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700263.png  || $\alpha \circ b = \alpha b + \sum _ { i = 1 } ^ { \infty } \phi _ { i } ( \alpha , b ) t ^ { i } , \quad \alpha , b \in V$ || $$ \alpha \circ b = \alpha b + \sum _ { i = 1 } ^ { \infty } \phi _ { i } ( \alpha , b ) t ^ { i } , \quad \alpha , b \in V, $$|| conf 0.097  F 
 
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| 23.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|96.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d030/d030700/d030700270.png  || $\Phi ( \alpha ) = \alpha + \sum _ { i = 1 } ^ { \infty } t ^ { i } \phi _ { i } ( \alpha ) , \quad \alpha \in V$ || $$ \Phi ( \alpha ) = \alpha + \sum _ { i = 1 } ^ { \infty } t ^ { i } \phi _ { i } ( \alpha ) , \quad \alpha \in V, $$|| conf 0.873  F 
 
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==[[Differential algebra]]==
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| 24.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|106.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830107.png  || $S ^ { t } F = \sum _ { j = 1 } ^ { r } c _ { j } A ^ { p _ { j } } A _ { 1 } ^ { i _ { 1 j } } \dots A _ { m - l } ^ { i _ { m - l } , j }$ || $$ S ^ { t } F = \sum _ { j = 1 } ^ { r } c _ { j } A ^ { p _ { j } } A _ { 1 } ^ { i _ { 1 j } } \dots A _ { m - l } ^ { i _ { { m - l } , j } },$$|| conf 0.149
 
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| 25.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|146.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830141.png  || $( \eta _ { 1 } , \ldots , \eta _ { k } ) \rightarrow F ( \zeta _ { 1 } , \ldots , \zeta _ { k } )$ || $ ( \eta _ { 1 } , \ldots , \eta _ { k } ) \rightarrow {}_{\cal F} ( \zeta _ { 1 } , \ldots , \zeta _ { k } ) $|| conf 0.562  F 
 
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| 26.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|145.]])$^F$*||  https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d031830150.png  || $( \eta _ { 1 } , \ldots , \eta _ { n } ) \rightarrow F ( \zeta _ { 1 } , \ldots , \zeta _ { n } )$ || $ ( \eta _ { 1 } , \ldots , \eta _ { n } ) \rightarrow {}_{\cal F} ( \zeta _ { 1 } , \ldots , \zeta _ { n } ) $|| conf 0.376  F 
 
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| 27.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|57.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183016.png  || $\omega _ { V } = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right)$ || $$ \omega _ { V } = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right), $$|| conf 0.780
 
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| 28.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|111.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d031/d031830/d03183043.png || $e _ { i j } = \operatorname { ord } _ { Y } _ { j } F _ { i } , \quad 1 \leq i \leq n , \quad i \leq j \leq n$ ||  $$ e_ { i j } = \operatorname { ord } _  { { Y } _ { j } } F _ { i } , \quad 1 \leq i \leq n , \quad i \leq j \leq n, $$ || conf 0.187 
 
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==[[Dimension polynomial]]==
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| 29.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|48.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d032/d032490/d03249029.png || $\omega _ { \eta / F } ( x ) = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right)$ ||  $$  \omega _ { \eta / F } ( x ) = \sum _ { 0 \leq i \leq m } \alpha _ { i } \left( \begin{array} { c } { x + i } \\ { i } \end{array} \right),   $$ || conf 0.968
 
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==[[Duality]]==
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| 30.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|118.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120173.png  || $H ^ { p } ( X , F ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) ) \rightarrow C$ || $$ H ^ { p } ( X , {\cal F} ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( {\cal F} , \Omega ) ) \rightarrow {\mathbf C}, $$|| conf 0.824  F 
 
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| 31.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|59.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120175.png  || $H ^ { p } ( X , F ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) ) \rightarrow H _ { c } ^ { n } ( X , \Omega )$ || $$ H ^ { p } ( X , {\cal F} ) \times H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( {\cal F} , \Omega ) ) \rightarrow H _ { c } ^ { n } ( X , \Omega ) $$|| conf 0.921  F 
 
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| 32.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|124.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120184.png  || $( H ^ { p } ( X , F ) ) ^ { \prime } \cong H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( F , \Omega ) )$ || $$ ( H ^ { p } ( X , {\cal F} ) ) ^ { \prime } \cong H _ { c } ^ { n - p } ( X , \operatorname { Hom } ( {\cal F} , \Omega ) ). $$|| conf 0.829  F 
 
d034120184.png (184)
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| 33.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|29.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120236.png  || $\beta : \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X  F  , \Omega ) \rightarrow \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X \backslash Y || F , \Omega )$ || $$ \beta : \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X ; {\cal F}  , \Omega ) \rightarrow \operatorname { Ext } _ { c } ^ { n - p - 1 } ( X \backslash Y ; {\cal F} , \Omega ). $$|| conf 0.634 || F
 
d034120236.png (236)
|-
| 34.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|77.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120247.png  || $\underset { n \rightarrow \infty } { \operatorname { lim } } | \alpha _ { n } | ^ { 1 / n } = \sigma < + \infty$ || $$ \underset { n \rightarrow \infty } { \overline { \lim } } | \alpha _ { n } | ^ { 1 / n } = \sigma < + \infty. $$|| conf 0.521  F 
 
d034120247.png (247)
|-
| 35.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|58.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120253.png  || $h ( \phi ) = \operatorname { lim } _ { r \rightarrow \infty } \frac { \operatorname { ln } | A ( r e ^ { i \phi } ) | } { r }$ || $$ h ( \phi ) = \underset { n\rightarrow \infty }{\overline{ \lim } } \frac { \operatorname { ln } | A ( r e ^ { i \phi } ) | } { r } $$|| conf 0.861  F 
 
d034120253.png (253)
|-
| 36.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|69.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120360.png  || $\operatorname { sup } _ { l \in E ^ { \perp } } | l ( \omega ) | = \operatorname { inf } _ { x \in E } \| \omega - x \|$ || $$ \operatorname* { sup } _ { l \in E^\perp \atop \|l\|\le 1 }  | l ( \omega ) | = \operatorname* { inf } _ { x \in E } \| \omega - x \|, $$|| conf 0.293   F 
 
d034120360.png (360)
|-
| 37.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|15.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120376.png  || $\operatorname { sup } _ { f \in B ^ { 1 } } | \int _ { \partial G } f ( \zeta ) \omega ( \zeta ) d \zeta | = \operatorname { inf } _ { \phi \in E ^ { 1 } } \int _ { \partial G } | \omega ( \zeta ) - \phi ( \zeta ) \| d \zeta |$ || $$ \operatorname* { sup } _ { f \in B ^ { 1 } } \big| \int\limits _ { \partial G } f ( \zeta ) \omega ( \zeta ) d \zeta \big| = \operatorname* { inf } _ { \phi \in E ^ { 1 } } \int\limits _ { \partial G } | \omega ( \zeta ) - \phi ( \zeta ) | | d \zeta |. $$|| conf 0.508
 
d034120376.png (376)
|-
| 38.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|52.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120509.png  || $f = \{ f _ { \alpha } \} \in \prod _ { \alpha } F _ { \alpha } , \quad g = \{ g _ { \alpha } \} \in \oplus _ { \alpha } G _ { \alpha }$ || $$ f = \{ f _ { \alpha } \} \in \prod _ { \alpha } F _ { \alpha } , \quad g = \{ g _ { \alpha } \} \in \operatorname*\oplus _ { \alpha } G _ { \alpha }. $$|| conf 0.491
 
d034120509.png (509)
|-
| 39.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|140.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120535.png  || $f ^ { * } ( x ^ { * } ) = \operatorname { sup } _ { x \in X } ( \langle x ^ { * } , x \rangle - f ( x ) )$ || $$ f ^ { * } ( x ^ { * } ) = \operatorname*{ sup } _ { x \in X } ( \langle x ^ { * } , x \rangle - f ( x ) ) $$|| conf 0.900
 
d034120535.png (535)
|-
| 40.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|94.]]) ||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d034120555.png  || $f _ { 0 } ( x ) \rightarrow \text { inf, } \quad f _ { i } ( x ) \leq 0 , \quad i = 1 , \ldots , m , \quad x \in B$ || $$ f _ { 0 } ( x ) \rightarrow \text { inf, } \quad f _ { i } ( x ) \leq 0 , \quad i = 1 , \ldots , m , \quad x \in B, $$|| conf 0.810
 
d034120555.png (555)
|-
| 41.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|74.]])*||  https://www.encyclopediaofmath.org/legacyimages/d/d034/d034120/d03412079.png  || $( c _ { \gamma } , c ^ { r } ) = \sum _ { t ^ { r } \in K } c _ { r } ( t ^ { \prime } ) c ^ { r } ( t ^ { r } ) \operatorname { mod } 1$ || $$ ( c _ { \gamma } , c ^ { r } ) = \sum _ { t ^ { r } \in K } c _ { r } ( t ^ { \prime } ) c ^ { r } ( t ^ { r } ) \operatorname { mod } 1 $$|| conf 0.117  F 
 
d03412079.png (79)
|-
|}

==[[Extension of a differential field]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F? 
png file 
|-
| 42.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|63.]]) ||  https://www.encyclopediaofmath.org/legacyimages/e/e036/e036960/e03696024.png || $F _ { 1 } F _ { 2 } = F _ { 1 } \langle F _ { 2 } \rangle = F _ { 1 } ( F _ { 2 } ) = F _ { 2 } ( F _ { 1 } ) = F _ { 2 } \langle F _ { 1 } \rangle$ ||  $$  F _ { 1 } F _ { 2 } = F _ { 1 } \langle F _ { 2 } \rangle = F _ { 1 } ( F _ { 2 } ) = F _ { 2 } ( F _ { 1 } ) = F _ { 2 } \langle F _ { 1 } \rangle,  $$ || conf 0.628
 
e03696024.png (24)
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|}

==[[Formal group]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 43.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|120.]])*||  https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f040820118.png || $\operatorname { og } F _ { MU } ( X ) = \sum _ { i = 1 } ^ { \infty } i ^ { - 1 } [ C ^ { - } P ^ { - 1 } ] X ^ { i }$ ||  $$ \operatorname { log } F _ {\rm MU } ( X ) = \sum _ { i = 1 } ^ { \infty } i ^ { - 1 } [ {\rm CP} ^ {i - 1 } ] X ^ { i }, $$ || conf 0.098  F 
 
f040820118.png (118)
|-
| 44.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|147.]])*||  https://www.encyclopediaofmath.org/legacyimages/f/f040/f040820/f04082059.png || $( x _ { 1 } , \ldots , x _ { x } ) \circ ( y _ { 1 } , \ldots , y _ { n } ) = ( z _ { 1 } , \ldots , z _ { x } )$ ||  $$  ( x _ { 1 } , \ldots , x _ { n } ) \circ ( y _ { 1 } , \ldots , y _ { n } ) = ( z _ { 1 } , \ldots , z _ { n } ), $$ || conf 0.553  F 
 
f04082059.png (59)
|-
|}

==[[Gel'fond-Schneider method]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 45.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|148.]]) ||  https://www.encyclopediaofmath.org/legacyimages/g/g130/g130020/g1300205.png || $\alpha ^ { \beta } = \operatorname { exp } \{ \beta \operatorname { log } \alpha \}$ ||  $   \alpha ^ { \beta } = \operatorname { exp } \{ \beta \operatorname { log } \alpha \}     $ || conf 0.979
 
g1300205.png (5)
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|}

==[[Group]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 46.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|22.]])*||  https://www.encyclopediaofmath.org/legacyimages/g/g045/g045210/g04521075.png || $\left. \begin{array} { l l l } { A } & { \rightarrow Y } & { \square } \\ { \downarrow } & { \square } & { } & { \square } \\ { X } & { \square } & { } & { A } \end{array} \right.$ || style="text-align: center;" | Source incomplete || conf 0.226  F 
 
g04521075.png (75)
|-
|}

==[[Homogeneous space]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
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!style=width: 7%| Confidence, F?
png file 
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| 47.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|89.]]) ||  https://www.encyclopediaofmath.org/legacyimages/h/h047/h047690/h04769069.png || $\mathfrak { g } = \mathfrak { f } + \mathfrak { m } , \quad \mathfrak { f } \cap \mathfrak { m } = \{ 0 \}$ ||  $$ \mathfrak { g } = \mathfrak { f } + \mathfrak { m } , \quad \mathfrak { f } \cap \mathfrak { m } = \{ 0 \}, $$ || conf 0.793
 
h04769069.png (69)
|-
|}

==[[Hopf algebra]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 48.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|103.]]) ||  https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970129.png || $m \circ ( \iota \otimes 1 ) \circ \mu = m \circ ( 1 \otimes \iota ) \circ \mu = e \circ \epsilon$ || $m \circ ( \iota \otimes 1 ) \circ \mu = m \circ ( 1 \otimes \iota ) \circ \mu = e \circ \epsilon$  || conf 0.618
 
h047970129.png (129)
|-
| 49.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|107.]])*||  https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h047970139.png || $F _ { 1 } ( X || Y ) , \ldots , F _ { n } ( X || Y ) \in K [ X _ { 1 } , \ldots , X _ { n } || Y _ { 1 } , \ldots , Y _ { n } ] \}$ || $F _ { 1 } ( X ; Y ) , \ldots , F _ { n } ( X ; Y ) \in K [ X _ { 1 } , \ldots , X _ { n } ; Y _ { 1 } , \ldots , Y _ { n } ] \}$ || conf 0.353  F 
 
h047970139.png (139)
|-
| 50.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|97.]]) ||  https://www.encyclopediaofmath.org/legacyimages/h/h047/h047970/h04797042.png || $\epsilon ( x ) = 0 , \quad \delta ( x ) = x \bigotimes 1 + 1 \bigotimes x , \quad x \in \mathfrak { g }$ ||  $$  \epsilon ( x ) = 0 , \quad \delta ( x ) = x \otimes 1 + 1 \otimes x , \quad x \in \mathfrak { g }.   $$ || conf 0.213
 
h04797042.png (42)
|-
|}

==[[Invariants, theory of]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
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!style=width: 7%| Confidence, F?
png file 
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| 51.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|149.]])*||  https://www.encyclopediaofmath.org/legacyimages/i/i052/i052350/i05235015.png || $\alpha _ { 1 } , \ldots , i _ { R } \rightarrow \alpha _ { 2 } ^ { \prime } , \ldots , i _ { R }$ ||  $$ \alpha _ { i_1,\dots, i_n }  \rightarrow \alpha _ { i_1, \dots, i_n} ^ { \prime }.     $$ || conf 0.142  F 
 
i05235015.png (15)
|-
|}

==[[Jordan algebra]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
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!style=width: 7%| Confidence, F?
png file 
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| 52.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|150.]]) ||  https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427030.png || $H ( C _ { 3 } , \Gamma ) = \{ X \in C _ { 3 } : X = \Gamma ^ { - 1 } X \square ^ { \prime } \Gamma \}$ ||  $$   ( C _ { 3 } , \Gamma ) = \big\{ X \in C _ { 3 } : X = \Gamma ^ { - 1 } X \square ^ { \prime } \Gamma \big\} ,     $$ || conf 0.651
 
j05427030.png (30)
|-
| 53.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|42.]]) ||  https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427031.png || $\Gamma = \operatorname { diag } \{ \gamma _ { 1 } , \gamma _ { 2 } , \gamma _ { 3 } \} , \quad \gamma _ { i } \neq 0 , \quad \gamma _ { i } \in F$ ||  $$  \Gamma = \operatorname { diag } \{ \gamma _ { 1 } , \gamma _ { 2 } , \gamma _ { 3 } \} , \quad \gamma _ { i } \neq 0 , \quad \gamma _ { i } \in F,       $$ || conf 0.987 
 
j05427031.png (31)
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| 54.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|125.]])*||  https://www.encyclopediaofmath.org/legacyimages/j/j054/j054270/j05427077.png || $\mathfrak { g } = \mathfrak { g } - 1 + \mathfrak { g } \mathfrak { d } + \mathfrak { g } _ { 1 }$ || $\mathfrak { g } = \mathfrak { g }_{ - 1} + \mathfrak { g }_0 + \mathfrak { g } _ { 1 }$       || conf 0.598  F 
 
j05427077.png (77)
|-
|}

==[[Jordan matrix]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
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| 55.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|6.]])*||  https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j0543403.png || $J = \left| \begin{array} { c c c c } { J _ { n _ { 1 } } ( \lambda _ { 1 } ) } & { \square } & { \square } & { \square } \\ { \square } & { \ldots } & { \square } & { 0 } \\ { 0 } & { \square } & { \ldots } & { \square } \\ { \square } & { \square } & { \square } & { J _ { n _ { S } } ( \lambda _ { s } ) } \end{array} \right|$ ||  $$J = \left\| \begin{array} { c c c c } 
 J_{n_1}(\lambda_1)  &   0     &    0   & 0 \\ 
       0             & \ddots  & \ddots & 0 \\
       0             & \ddots  & \ddots & 0 \\
       0             &   0     &    0   & J_{n_s}(\lambda_s)
\end{array} \right\|,$$ || conf 0.072  F 
 
j0543403.png (3)
|-
| 56.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|64.]]) ||  https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j05434030.png || $C _ { m } ( \lambda ) = \operatorname { rk } ( A - \lambda E ) ^ { m - 1 } - 2 \operatorname { rk } ( A - \lambda E ) ^ { m } +$ ||  $$\empty$$ || conf 0.955
 
j05434030.png (30)
|-
| 57.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|1.]])*||  https://www.encyclopediaofmath.org/legacyimages/j/j054/j054340/j0543406.png || $J _ { m } ( \lambda ) = \| \begin{array} { c c c c c c } { \lambda } & { 1 } & { \square } & { \square } & { \square } & { \square } \\ { \square } & { \lambda } & { 1 } & { \square } & { 0 } & { \square } \\ { \square } & { \square } & { \cdots } & { \square } & { \square } & { \square } \\ { \square } & { \square } & { \square } & { \cdots } & { \square } & { \square } \\ { \square } & { 0 } & { \square } & { \square } & { \lambda } & { 1 } \\ { \square } & { \square } & { \square } & { \square } & { \square } & { \lambda } \end{array} ]$ || $$J_m(\lambda) = \left\| \begin{array} { c c c c c c }
\lambda &    1    & \square &  \square &  \square &  \square \\
\square & \lambda &    1    &  \square &   0      &  \square \\
\square & \square & \ddots  &  \ddots  &  \square &  \square\\
\square & \square & \square &  \ddots  &  \ddots  &  \square \\
\square &   0     & \square &  \square & \lambda  &  1 \\
\square & \square & \square &  \square &  \square & \lambda
\end{array} \right\|,$$ || conf 0.098  F 
 
j0543406.png (6)
|-
|}
==[[Lie algebra, semi-simple]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
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| 58.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|5.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510127.png || $\left\| \begin{array} { r r r r r r } { 2 } & { - 1 } & { 0 } & { \dots } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 1 } & { \dots } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { \dots } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 2 } & { - 2 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 2 } \end{array} \right\|$ || $$B_n: \quad \left\| \begin{array} { r r r r r r }
{ 2 }   & { - 1 } & { 0 }   & { \dots } & { 0 } & { 0 }  \\ 
{ - 1 } & { 2 }   & { - 1 } & { \dots } & { 0 } & { 0 }  \\ 
{ 0 }   & { - 1 } & { 2 }   & { \dots } & { 0 } & { 0 }  \\ 
 \cdot  & \cdot   & \cdot   &   \dots   & \cdot & \cdot  \\
{ 0 }   & { 0 }   & { 0 }   & { \dots } & { - 1 } & { 0 }\\ 
{ 0 }   & { 0 }   & { 0 }   & { \dots } & { 2 } & { - 2 }\\ 
{ 0 }   & { 0 }   & { 0 }   & { \dots } & { - 1 } & { 2 } 
\end{array} \right\|,$$|| conf 0.232
 
l058510127.png (127)
|-
| 59.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|3.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510129.png || $\| \left. \begin{array} { r r r r r r r } { 2 } & { - 1 } & { 0 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 1 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 2 } & { - 1 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 2 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 0 } & { 2 } \end{array} \right. |$ ||  $$D_n: \quad 
\left\| \begin{array} { r r r r r r r } 
{ 2 } & { - 1 } & { 0 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 } \\ 
{ - 1 } & { 2 } & { - 1 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 }\\ 
{ 0 } & { - 1 } & { 2 } & { \dots } & { 0 } & { 0 } & { 0 } & { 0 }  \\ 
\cdot  & \cdot   & \cdot  &   \dots   & \cdot & \cdot &\cdot & \cdot \\
{ 0 } & { 0 } & { 0 } & { \dots } & { 2 } & { - 1 } & { 0 } & { 0 }  \\ 
{ 0 } & { 0 } & { 0 } & { \dots } & { - 1 } & { 2 } & { - 1 } & { - 1 }\\ 
{ 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 2 } & { 0 } \\ 
{ 0 } & { 0 } & { 0 } & { \dots } & { 0 } & { - 1 } & { 0 } & { 2 } 
\end{array} \right\|,$$ || conf 0.055  F 

l058510129.png (129)
|-
| 60.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|8.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510130.png || $\left\| \begin{array} { r r r r r r } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } \\ { - 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\|$ || $$E_6: 
\quad \left\| \begin{array} { r r r r r r } 
{ 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ 
{ 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } \\ 
{ - 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ 
{ 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ 
{ 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ 
{ 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } 
\end{array} \right\|,$$ || conf 0.628  F

l058510130.png (130)
|-
| 61.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|4.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510131.png || $\left\| \begin{array} { r r r r r r r } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\|$ || $$E_7: \quad 
\left\| \begin{array} { r r r r r r r } 
{ 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ 
{ 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ 
{-1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ 
{ 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ 
{ 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ 
{ 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ 
{ 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } 
\end{array} \right\|,$$ || conf 0.278
 
l058510131.png (131)
|-
| 62.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|2.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510132.png || $\left. \begin{array} { r l l l l l l l } { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right.$ || $$E_8: \quad 
\left\| \begin{array} { r r r r r r r r } 
{ 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } & 
{ 0 } \\ { 0 } & { 2 } & { 0 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ 
{-1 } & { 0 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } & { 0 } \\ 
{ 0 } & { - 1 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } & { 0 } \\ 
{ 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } & { 0 } \\ 
{ 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } & { 0 } \\ 
{ 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } & { - 1 } \\ 
{ 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { 0 } & { - 1 } & { 2 } 
\end{array} \right\|,$$ || conf 0.354  F 
 
l058510132.png (132)
|-
| 63.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|10.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l058510133.png || $\left\| \begin{array} { r r r r } { 2 } & { - 1 } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 2 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\| , \quad G _ { 2 } : \quad \left\| \begin{array} { r r } { 2 } & { - 1 } \\ { - 3 } & { 2 } \end{array} \right\|$ 
|| $$F_4: \quad \left\| \begin{array} { r r r r } { 2 } & { - 1 } & { 0 } & { 0 } \\ { - 1 } & { 2 } & { - 2 } & { 0 } \\ { 0 } & { - 1 } & { 2 } & { - 1 } \\ { 0 } & { 0 } & { - 1 } & { 2 } \end{array} \right\| , \quad G _ { 2 } : \quad \left\| \begin{array} { r r } { 2 } & { - 1 } \\ { - 3 } & { 2 } \end{array} \right\|.$$ || conf 0.374  F 
 
l058510133.png (133)
|-
| 64.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|98.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851030.png  || $\mathfrak { g } _ { \alpha } = \{ X \in \mathfrak { g } : [ H , X ] = \alpha ( H ) X , H \in \mathfrak { h } \}$ || $$ \mathfrak { g } _ { \alpha } = \{ X \in \mathfrak { g } : [ H , X ] = \alpha ( H ) X , H \in \mathfrak { h } \}. $$|| conf 0.976
 
l05851030.png (30)
|-
| 65.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|126.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851037.png  || $\mathfrak { g } = \mathfrak { h } + \sum _ { \alpha \in \Sigma } \mathfrak { g } _ { \alpha }$ || $$ \mathfrak { g } = \mathfrak { h } + \sum _ { \alpha \in \Sigma } \mathfrak { g } _ { \alpha } .$$|| conf 0.945
 
l05851037.png (37)
|-
| 66.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|61.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851044.png  || $\mathfrak { g } _ { \alpha } = \operatorname { dim } [ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { - \alpha } ] = 1$ || $$ \mathfrak { g } _ { \alpha } = \operatorname { dim } [ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { - \alpha } ] = 1 .$$|| conf 0.520  F 
 
l05851044.png (44)
|-
| 67.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|65.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851050.png  || $[ H _ { \alpha } , X _ { \alpha } ] = 2 X _ { \alpha } \quad \text { and } \quad [ H _ { \alpha } , Y _ { \alpha } ] = - 2 Y _ { 0 }$ || $$ [ H _ { \alpha } , X _ { \alpha } ] = 2 X _ { \alpha } \quad {\rm and } \quad [ H _ { \alpha } , Y _ { \alpha } ] = - 2 Y _ { \alpha }. $$|| conf 0.539  F 
 
l05851050.png (50)
|-
| 68.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|70.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851051.png  || $\beta ( H _ { \alpha } ) = \frac { 2 ( \alpha , \beta ) } { ( \alpha , \alpha ) } , \quad \alpha , \beta \in \Sigma$ || $$ \beta ( H _ { \alpha } ) = \frac { 2 ( \alpha , \beta ) } { ( \alpha , \alpha ) } , \quad \alpha , \beta \in \Sigma, $$|| conf 0.997
 
l05851051.png (51)
|-
| 69.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|112.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851057.png  || $[ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { \beta } ] = \mathfrak { g } _ { \alpha + \beta }$ || $$ [ \mathfrak { g } _ { \alpha } , \mathfrak { g } _ { \beta } ] = \mathfrak { g } _ { \alpha + \beta } $$|| conf 0.917
 
l05851057.png (57)
|-
| 70.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|127.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851064.png  || $H _ { \alpha _ { 1 } } , \ldots , H _ { \alpha _ { k } } , X _ { \alpha } \quad ( \alpha \in \Sigma )$ || $$ H _ { \alpha _ { 1 } } , \ldots , H _ { \alpha _ { k } } , X _ { \alpha } \quad ( \alpha \in \Sigma ) $$|| conf 0.432
 
l05851064.png (64)
|-
| 71.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|113.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851069.png  || $[ [ X _ { \alpha _ { i } } , X _ { - } \alpha _ { i } ] , X _ { - \alpha _ { j } } ] = - n ( i , j ) X _ { \alpha _ { j } }$ || $$ [ [ X _ { \alpha _ { i } } , X _ { - } \alpha _ { i } ] , X _ { - \alpha _ { j } } ] = - n ( i , j ) X _ { \alpha _ { j } }, $$|| conf 0.628  F 
 
l05851069.png (69)
|-
| 72.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|79.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851073.png  || $n ( i , j ) = \alpha _ { j } ( H _ { i } ) = \frac { 2 ( \alpha _ { i } , \alpha _ { j } ) } { ( \alpha _ { j } , \alpha _ { j } ) }$ || $$ n ( i , j ) = \alpha _ { j } ( H _ { i } ) = \frac { 2 ( \alpha _ { i } , \alpha _ { j } ) } { ( \alpha _ { j } , \alpha _ { j } ) }. $$|| conf 0.992
 
l05851073.png (73)
|-
| 73.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|13.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851074.png  || $[ X _ { \alpha } , X _ { \beta } ] = \left\{ \begin{array} { l l } { N _ { \alpha , \beta } X _ { \alpha + \beta } } & { \text { if } \alpha + \beta \in \Sigma } \\ { 0 } & { \text { if } \alpha + \beta \notin \Sigma } \end{array} \right.$ || $$ [ X _ { \alpha } , X _ { \beta } ] = \left\{ \begin{array} { l l } { N _ { \alpha , \beta } X _ { \alpha + \beta } } & { \text { if } \alpha + \beta \in \Sigma, } \\ { 0 } & { \text { if } \alpha + \beta \notin \Sigma, } \end{array} \right. $$|| conf 0.988
 
l05851074.png (74)
|-
| 74.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|80.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851078.png  || $N _ { \alpha , \beta } = - N _ { - \alpha , - \beta } \quad \text { and } \quad N _ { \alpha , \beta } = \pm ( p + 1 )$ || $$ N _ { \alpha , \beta } = - N _ { - \alpha , - \beta } \quad  {\rm and } \quad N _ { \alpha , \beta } = \pm ( p + 1 ), $$|| conf 0.961
 
l05851078.png (78)
|-
| 75.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|85.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058510/l05851085.png  || $X _ { \alpha } - X _ { - \alpha } , \quad i ( X _ { \alpha } + X _ { - \alpha } ) \quad ( \alpha \in \Sigma _ { + } )$ || $$ iH_\alpha, X _ { \alpha } - X _ { - \alpha } , \quad i ( X _ { \alpha } + X _ { - \alpha } ) \quad ( \alpha \in \Sigma _ { + } ) $$|| conf 0.691  F 
 
l05851085.png (85)
|-
|}

==[[Lie algebra, solvable]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
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!style=width: 7%| Confidence, F?
png file 
|-
| 76.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|119.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852011.png || $[ \mathfrak { g } _ { i } , \mathfrak { g } _ { i } ] \subset \mathfrak { g } _ { \mathfrak { i } } + 1$ ||  $  [ \mathfrak { g } _ { i } , \mathfrak { g } _ { i } ] \subset \mathfrak {g}_{ i  + 1 }  $ || conf 0.276  F 
 
l05852011.png (11)
|-
| 77.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|141.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058520/l05852046.png || $\operatorname { dim } \mathfrak { g } _ { i } = \operatorname { dim } \mathfrak { g } - i$ ||  $ \operatorname { dim } \mathfrak { g } _ { i } = \operatorname { dim } \mathfrak { g } - i   $ || conf 0.901
 
l05852046.png (46)
|-
|}

==[[Lie group]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
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!style=width: 7%| Confidence, F?
png file 
|-
| 78.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|62.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l058590115.png || $( G ) \cong \operatorname { Aut } ( L ( G ) ) \quad \text { and } \quad L ( \operatorname { Aut } ( G ) ) \cong D ( L ( G ) )$ ||  $$ \operatorname { Aut } ( G ) \cong \operatorname { Aut } ( L ( G ) ) \quad  {\rm and } \quad L ( \operatorname { Aut } ( G ) ) \cong D ( L ( G ) ),     $$ || conf 0.693  F 
 
l058590115.png (115)
|-
| 79.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|50.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058590/l05859086.png || $( X , Y ) \rightarrow \operatorname { exp } ^ { - 1 } ( \operatorname { exp } X \operatorname { exp } Y ) , \quad X , Y \in L ( G )$ ||  $$  ( X , Y ) \rightarrow \operatorname { exp } ^ { - 1 } ( \operatorname { exp } X \operatorname { exp } Y ) , \quad X , Y \in L ( G ),        $$ || conf 0.856
 
l05859086.png (86)
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|}

==[[Lie group, compact]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
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!style=width: 7%| Confidence, F?
png file 
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| 80.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|121.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058610/l05861012.png || $J = \left\| \begin{array} { c c } { 0 } & { E _ { x } } \\ { - E _ { x } } & { 0 } \end{array} \right\|$ ||  $$\empty$$ || conf 0.364  F 
 
l05861012.png (12)
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|}
==[[Lie group, nilpotent]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
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!style=width: 7%| Confidence, F?
png file 
|-
| 81.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|83.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058660/l0586604.png || $N ( F ) = \{ g \in GL ( V ) : g v \equiv v \operatorname { mod } V _ { i } \text { for all } v \in V _ { i } , i \geq 1 \}$ ||  $$\empty$$ || conf 0.466
 
l0586604.png (4)
|-
|}
==[[Lie group, semi-simple]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 82.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|35.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l058680102.png || $L ( \mathfrak { g } ) \cong \Gamma _ { 0 } ( \mathfrak { u } ) \cap \mathfrak { h } ^ { \prime } / \Gamma _ { 0 } ( [ \mathfrak { k } , \mathfrak { k } ] )$ ||  $$\empty$$ || conf 0.659  F 
 
l058680102.png (102)
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| 83.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|81.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058680/l05868032.png || $\Gamma _ { 1 } = \Gamma _ { 1 } ( g ) = \{ X \in h : \alpha ( X ) \in 2 \pi i Z \text { for all } \alpha \in \Sigma \}$ ||  $$\empty$$ || conf 0.183  F 
 
l05868032.png (32)
|-
|}
==[[Lie p-algebra]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
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| 84.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|36.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872026.png || $( \operatorname { ad } x ) ^ { n } y = \sum _ { j = 1 } ^ { n } ( - 1 ) ^ { j } \left( \begin{array} { c } { n } \\ { j } \end{array} \right) x ^ { n - j } y x ^ { j }$ ||  $$\empty$$ || conf 0.356
 
l05872026.png (26)
|-
| 85.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|99.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058720/l05872078.png || $\pi ( x + y ) = \pi ( x ) + \pi ( y ) , \quad \pi ( \lambda x ) = \lambda ^ { p } \pi ( x ) , \quad \lambda \in k$ ||  $$\empty$$ || conf 0.964
 
l05872078.png (78)
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|}
==[[Lie theorem]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 86.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|134.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876010.png || $y _ { i } = f _ { i } ( g _ { 1 } , \ldots , g _ { i } || x _ { 1 } , \ldots , x _ { n } ) , \quad i = 1 , \ldots , n$ ||  $$\empty$$ || conf 0.276
 
l05876010.png (10)
|-
| 87.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|86.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876016.png || $X _ { i } = \sum _ { j = 1 } ^ { n } \xi _ { i j } ( x ) \frac { \partial } { \partial x _ { j } } , \quad i = 1 , \ldots , r$ ||  $$\empty$$ || conf 0.656
 
l05876016.png (16)
|-
| 88.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|66.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876030.png || $\frac { \partial f _ { j } } { \partial g _ { i } } ( g , x ) = \sum _ { k = 1 } ^ { r } \xi _ { k j } ( f ( g _ { s } x ) ) \psi _ { k i } ( g )$ ||  $$\empty$$ || conf 0.336  F 
 
l05876030.png (30)
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| 89.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|19.]])*||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876037.png || $\sum _ { k = 1 } ^ { N } ( \xi _ { i k } \frac { \partial \xi _ { j l } } { \partial x _ { k } } - \xi _ { j k } \frac { \partial \xi _ { i l } } { \partial x _ { k } } ) = \sum _ { k = 1 } ^ { r } c _ { i j } ^ { k } \xi _ { k l }$ ||  $$\empty$$ || conf 0.157  F 
 
l05876037.png (37)
|-
| 90.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|14.]]) ||  https://www.encyclopediaofmath.org/legacyimages/l/l058/l058760/l05876052.png || $\left. \begin{array} { c } { c _ { i j } ^ { k } = - c _ { j i } ^ { k } } \\ { \sum _ { l = 1 } ^ { r } ( c _ { i l } ^ { m } c _ { j k } ^ { l } + c _ { k l } ^ { m } c _ { i j } ^ { l } + c _ { j l } ^ { m } c _ { k i } ^ { l } ) = 0 , \quad 1 \leq i , j , k , l , m \leq r } \end{array} \right.$ ||  $$\empty$$ || conf 0.085
 
l05876052.png (52)
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|}
==[[Maximal torus]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
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| 91.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|95.]]) ||  https://www.encyclopediaofmath.org/legacyimages/m/m063/m063010/m06301072.png || $F ( x _ { 1 } f _ { 1 } + \ldots + x _ { x } f _ { n } ) = x _ { 1 } x _ { n } + x _ { 2 } x _ { n } - 1 + \ldots + x _ { p } x _ { n } - p + 1$ ||  $$\empty$$ || conf 0.198
 
m06301072.png (72)
|-
|}
==[[Non-Abelian cohomology]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 92.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|114.]])*||  https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900110.png || $\phi ( g _ { 1 } ) \phi ( g ) \phi ( g _ { 1 } g _ { 2 } ) ^ { - 1 } = \operatorname { Int } m ( g _ { 1 } , g _ { 2 } )$ ||  $$\empty$$ || conf 0.443  F 
 
n066900110.png (110)
|-
| 93.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|90.]])*||  https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n066900118.png || $( g _ { 1 } , g _ { 2 } ) = h ( g _ { 1 } ) ( \phi ( g _ { 1 } ) ( h ( g _ { 2 } ) ) ) m ( g _ { 1 } , g _ { 2 } ) h ( g _ { 1 } , g _ { 2 } ) ^ { - 1 }$ ||  $$\empty$$ || conf 0.764  F 
 
n066900118.png (118)
|-
| 94.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|44.]]) ||  https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690016.png || $\delta ( e ) = e \quad \text { and } \quad \delta ( \rho ( a ) b ) = \sigma ( a ) \delta ( b ) , \quad \alpha \in C ^ { 0 } , \quad b \in C ^ { 1 }$ ||  $$\empty$$ || conf 0.400
 
n06690016.png (16)
|-
| 95.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|60.]])*||  https://www.encyclopediaofmath.org/legacyimages/n/n066/n066900/n06690028.png || $C ^ { * } ( \mathfrak { U } , F ) = ( C ^ { 0 } ( \mathfrak { U } , F ) , C ^ { 1 } ( \mathfrak { U } , F ) , C ^ { 2 } ( \mathfrak { U } , F ) )$ ||  $$\empty$$ || conf 0.205  F 
 
n06690028.png (28)
|-
|}
==[[Picard scheme]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 96.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|39.]])*||  https://www.encyclopediaofmath.org/legacyimages/p/p072/p072670/p07267025.png || $\operatorname { Pic } _ { X / k } ( S ^ { \prime } ) = \operatorname { Fic } ( X \times k S ^ { \prime } ) / \operatorname { Fic } ( S ^ { \prime } )$ ||  $$\empty$$ || conf 0.345  F +
 
p07267025.png (25)
|-
|}
==[[Principal analytic fibration]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 97.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|100.]])*||  https://www.encyclopediaofmath.org/legacyimages/p/p074/p074640/p07464025.png || $g j : U _ { i } \cap U _ { j } \rightarrow G , \quad i , j \in I , \quad U _ { i } \cap U _ { j } \neq \emptyset$ ||  $$\empty$$ || conf 0.184  F 
 
p07464025.png (25)
|-
|}
==[[Quantum groups]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 98.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|101.]]) ||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631062.png || $\phi ^ { * } : \mathfrak { g } ^ { * } \otimes \mathfrak { g } ^ { * } \rightarrow \mathfrak { g } ^ { * }$ ||  $$\empty$$ || conf 0.837
 
q07631062.png (62)
|-
| 99.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|108.]]) ||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631071.png || $\delta : U _ { \mathfrak { g } } \rightarrow U _ { \mathfrak { g } } \otimes U _ { \mathfrak { g } }$ ||  $$\empty$$ || conf 0.648
 
q07631071.png (71)
|-
| 100.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|56.]])*||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631072.png || $\delta ( \alpha ) = \operatorname { lim } _ { h \rightarrow 0 } h ^ { - 1 } ( \Delta ( a ) - \Delta ^ { \prime } ( \alpha ) )$ ||  $$\empty$$ || conf 0.304  F 
 
q07631072.png (72)
|-
| 101.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|129.]])*||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631088.png || $[ \alpha , X _ { i } ^ { \pm } ] = \pm \alpha _ { i } ( \alpha ) X _ { i } ^ { \pm } \quad \text { for } a$ ||  $$\empty$$ || conf 0.544  F 
 
q07631088.png (88)
|-
| 102.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|128.]]) ||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631089.png || $[ X _ { i } ^ { + } , X _ { j } ^ { - } ] = 2 \delta _ { i j } h ^ { - 1 } \operatorname { sinh } ( h H _ { i } / 2 )$ ||  $$\empty$$ || conf 0.893
 
q07631089.png (89)
|-
| 103.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|20.]]) ||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631092.png || $\sum _ { k = 0 } ^ { n } ( - 1 ) ^ { k } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) q ^ { - k ( n - k ) / 2 } ( X _ { i } ^ { \pm } ) ^ { k } X _ { j } ^ { \pm } \cdot ( X _ { i } ^ { \pm } ) ^ { n - k } = 0$ ||  $$\empty$$ || conf 0.055
 
q07631092.png (92)
|-
| 104.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|30.]]) ||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631095.png || $\left( \begin{array} { l } { n } \\ { k } \end{array} \right) _ { q } = \frac { ( q ^ { n } - 1 ) \ldots ( q ^ { n - k + 1 } - 1 ) } { ( q ^ { k } - 1 ) \ldots ( q - 1 ) }$ ||  $$\empty$$ || conf 0.443
 
q07631095.png (95)
|-
| 105.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|21.]])*||  https://www.encyclopediaofmath.org/legacyimages/q/q076/q076310/q07631099.png || $\Delta ( X _ { i } ^ { \pm } ) = X _ { i } ^ { \pm } \bigotimes \operatorname { exp } ( \frac { h H _ { i } } { 4 } ) + \operatorname { exp } ( \frac { - h H _ { i } } { 4 } ) \otimes x _ { i } ^ { \pm }$ ||  $$\empty$$ || conf 0.212  F 
 
q07631099.png (99)
|-
|}
==[[Rational representation]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 106.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|91.]]) ||  https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r077630100.png || $0 \leq \frac { 2 ( \chi , \alpha ) } { ( \alpha , \alpha ) } < p \quad \text { for all } \alpha \in \Delta$ ||  $$\empty$$ || conf 0.879
 
r077630100.png (100)
|-
| 107.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|135.]]) ||  https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r077630104.png || $\phi _ { 0 } \bigotimes \phi _ { 1 } ^ { Fr } \otimes \ldots \otimes \phi _ { d } ^ { FF ^ { d } }$ ||  $$\empty$$ || conf 0.136
 
r077630104.png (104)
|-
| 108.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|45.]])*||  https://www.encyclopediaofmath.org/legacyimages/r/r077/r077630/r07763055.png || $\chi = \delta _ { \phi } - \sum _ { \alpha \in \Delta } m _ { \alpha } \alpha , \quad m _ { \alpha } \in Z , \quad m _ { \alpha } \geq 0$ ||  $$\empty$$ || conf 0.862  F 
 
r07763055.png (55)
|-
|}
==[[Singular point]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 109.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|31.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590225.png || $\sum _ { k _ { 1 } , \ldots , k _ { n } = 0 } ^ { \infty } c _ { k _ { 1 } \cdots k _ { n } } ( z _ { 1 } - \zeta _ { 1 } ) ^ { k _ { 1 } } \ldots ( z _ { n } - \zeta _ { n } ) ^ { k _ { n } }$ ||  $$\empty$$ || conf 0.324
 
s085590225.png (225)
|-
| 110.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|46.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590404.png || $\frac { m _ { 1 } } { n _ { 1 } } < \frac { m _ { 2 } } { n _ { 1 } n _ { 2 } } < \ldots < \frac { m _ { g } } { n _ { 1 } \ldots n _ { g } } = \frac { m _ { g } } { n }$ ||  $$\empty$$ || conf 0.459
 
s085590404.png (404)
|-
| 111.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|115.]])*||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590429.png || $p ( Z ) = 1 - \operatorname { dim } H ^ { 0 } ( Z , O _ { Z } ) + \operatorname { dim } H ^ { 1 } ( Z , O _ { Z } )$ ||  $$\empty$$ || conf 0.997  F 
 
s085590429.png (429)
|-
| 112.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|136.]])*||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590440.png || $X _ { \epsilon } = \{ ( x _ { 0 } , \ldots , x _ { x } ) : f ( x _ { 0 } , \ldots , x _ { x } ) = \epsilon \}$ ||  $$\empty$$ || conf 0.433  F 
 
s085590440.png (440)
|-
| 113.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|12.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590458.png || $= \left\{ \begin{array} { l l } { ( x + \lambda ) ^ { 2 } \ldots ( x + k \lambda ) ^ { 2 } } & { \text { if } \mu = 2 k } \\ { ( x + \lambda ) ^ { 2 } \ldots ( x + k \lambda ) ^ { 2 } ( x + ( k + 1 ) \lambda ) } & { \text { if } \mu = 2 k + 1 } \end{array} \right.$ ||  $$\empty$$ || conf 0.870
 
s085590458.png (458)
|-
| 114.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|75.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590482.png || $( \frac { \partial F ( x , y , \lambda ) } { \partial x } , \frac { \partial F ( x , y , \lambda ) } { \partial y } )$ ||  $$\empty$$ || conf 0.986
 
s085590482.png (482)
|-
| 115.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|137.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590515.png || $\frac { d x _ { i } } { d x _ { i _ { 0 } } } = f _ { i } ( x ) , \quad f _ { i } \in C ( U ) , \quad i \neq i _ { 0 }$ ||  $$\empty$$ || conf 0.594
 
s085590515.png (515)
|-
| 116.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|142.]])*||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590527.png || $A = \| \left. \begin{array} { l l } { \alpha } & { b } \\ { c } & { e } \end{array} \right. |$ ||  $$\empty$$ || conf 0.506  F 
 
s085590527.png (527)
|-
| 117.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|53.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590634.png || $\Delta = ( F _ { x x } ^ { \prime \prime } ) _ { 0 } ( F _ { y y } ^ { \prime \prime } ) _ { 0 } - ( F _ { x y } ^ { \prime \prime } ) _ { 0 } ^ { 2 }$ ||  $$\empty$$ || conf 0.920
 
s085590634.png (634)
|-
| 118.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|16.]])*||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590645.png || $\left| \begin{array} { l l l } { F _ { X } ^ { \prime } } & { F _ { y } ^ { \prime } } & { F _ { z } ^ { \prime } } \\ { G _ { \chi } ^ { \prime } } & { G _ { y } ^ { \prime } } & { G _ { Z } ^ { \prime } } \end{array} \right|$ ||  $$\empty$$ || conf 0.230  F 
 
s085590645.png (645)
|-
| 119.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|92.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s085/s085590/s085590653.png || $( F _ { X } ^ { \prime } ) _ { 0 } = 0 , \quad ( F _ { y } ^ { \prime } ) _ { 0 } = 0 , \quad ( F _ { z } ^ { \prime } ) _ { 0 } = 0$ ||  $$\empty$$ || conf 0.300
 
s085590653.png (653)
|-
|}
==[[Solv manifold]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 120.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|138.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s086/s086100/s08610054.png || $\{ e \} \rightarrow \Delta \rightarrow \pi \rightarrow Z ^ { s } \rightarrow \{ e \}$ ||  $$\empty$$ || conf 0.972
 
s08610054.png (54)
|-
|}
==[[Stability theorems in algebraic K-theory]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
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!style=width: 7%| Confidence, F?
png file 
|-
| 121.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|71.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s087/s087060/s08706033.png || $\psi _ { t _ { 1 } , \ldots , t _ { R } } ^ { \prime } : S K _ { 1 } ( R ) \rightarrow S K _ { 1 } ( R ( t _ { 1 } , \ldots , t _ { n } ) )$ ||  $$\empty$$ || conf 0.379
 
s08706033.png (33)
|-
|}
==[[Steinberg module]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 122.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|130.]]) ||  https://www.encyclopediaofmath.org/legacyimages/s/s130/s130530/s13053016.png || $e = \frac { | U | } { | G | } ( \sum _ { b \in B } b ) ( \sum _ { w \in W } \operatorname { sign } ( w ) w )$ ||  $$\empty$$ || conf 0.138
 
s13053016.png (16)
|-
|}
==[[Steinberg symbol]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 123.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|24.]])*||  https://www.encyclopediaofmath.org/legacyimages/s/s130/s130540/s13054017.png || $( x _ { i j } ( a ) , x _ { k l } ( b ) ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } i \neq 1 , j \neq k } \\ { x _ { 1 } ( a b ) } & { \text { if } i \neq 1 , j = k } \end{array} \right.$ ||  $$\empty$$ || conf 0.381  F 
 
s13054017.png (17)
|-
|}
==[[Tilting theory]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 124.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|84.]]) ||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130130/t130130105.png || $0 \rightarrow \Lambda \rightarrow T _ { 1 } \rightarrow \ldots \rightarrow T _ { n } \rightarrow 0$ ||  $$\empty$$ || conf 0.946
 
t130130105.png (105)
|-
|}
==[[Tits quadratic form]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
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!style=width: 7%| Confidence, F?
png file 
|-
| 125.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|18.]]) ||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140104.png || $q R ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { i } x _ { j } + \sum _ { \langle \beta : i \rightarrow j ) \in Q _ { 1 } } x _ { , j } x _ { i } x _ { j }$ ||  $$\empty$$ || conf 0.112
 
t130140104.png (104)
|-
| 126.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|40.]]) ||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140118.png || $[ X ] \mapsto \chi _ { R } ( [ X ] ) = \sum _ { m = 0 } ^ { \infty } ( - 1 ) ^ { m } \operatorname { dim } _ { K } \operatorname { Ext } _ { R } ^ { m } ( X , X )$ ||  $$\empty$$ || conf 0.116 
 
t130140118.png (118)
|-
| 127.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|132.]])*||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140119.png || $\operatorname { dim } _ { 1 } : K _ { 0 } ( \operatorname { mod } R ) \rightarrow Z ^ { Q _ { 0 } }$ ||  $$\empty$$ || conf 0.287 F 
 
t130140119.png (119)
|-
| 128.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|37.]])*||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t130140140.png || $q ( x ) = \sum _ { i \in I } x _ { i } ^ { 2 } + \sum _ { i \prec j } x _ { i } x _ { j } - \sum _ { p \in \operatorname { max } l } ( \sum _ { i \prec p } x _ { i } ) x _ { p }$ ||  $$\empty$$ || conf 0.197  F 
 
t130140140.png (140)
|-
| 129.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|131.]])*||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014044.png || $X \mapsto \operatorname { dim } X = ( \operatorname { dim } _ { K } X _ { j } ) _ { j \in Q _ { 0 } }$ ||  $$\empty$$ || conf 0.819  F 
 
t13014044.png (44)
|-
| 130.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|25.]]) ||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014048.png || $[ X ] \mapsto \chi _ { Q } ( [ X ] ) = \operatorname { dim } _ { K } \operatorname { End } _ { Q } ( X ) - \operatorname { dim } _ { K } \operatorname { Ext } _ { Q } ^ { 1 } ( X , X )$ ||  $$\empty$$ || conf 0.661
 
t13014048.png (48)
|-
| 131.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|38.]])*||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t13014056.png || $A _ { Q } ( v ) = \prod _ { i , j \in Q _ { 0 } } \prod _ { \langle \beta : j \rightarrow i \rangle \in Q _ { 1 } } M _ { v _ { i } \times v _ { j } } ( K ) _ { \beta }$ ||  $$\empty$$ || conf 0.481  F 
 
t13014056.png (56)
|-
| 132.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|139.]])*||  https://www.encyclopediaofmath.org/legacyimages/t/t130/t130140/t1301406.png || $\Phi ( x ) = \sum _ { j \in Q _ { 0 } } x _ { j } ^ { 2 } - \sum _ { i , j \in Q _ { 0 } } d _ { i j } x _ { i } x _ { j }$ ||  $$\empty$$ || conf 0.648  F 
 
t1301406.png (6)
|-
|}
==[[Torus]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 133.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|41.]])*||  https://www.encyclopediaofmath.org/legacyimages/t/t093/t093350/t0933502.png || $r = \alpha \operatorname { sin } u k + l ( 1 + \epsilon \operatorname { cos } u ) ( i \operatorname { cos } v + j \operatorname { sin } v )$ ||  $$\empty$$ || conf 0.585  F 
 
t0933502.png (2)
|-
| 134.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|122.]])*||  https://www.encyclopediaofmath.org/legacyimages/t/t093/t093350/t0933507.png || $d s ^ { 2 } = \alpha ^ { 2 } d u ^ { 2 } + l ^ { 2 } ( 1 + \epsilon \operatorname { cos } u ) ^ { 2 } d v ^ { 2 }$ ||  $$\empty$$ || conf 0.696  F 
 
t0933507.png (7)
|-
|}
==[[Uniform distribution]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
|-
| 135.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|9.]]) ||  https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524027.png || $u _ { 3 } ( x ) = \left\{ \begin{array} { l l } { \frac { x ^ { 2 } } { 2 } , } & { 0 \leq x < 1 } \\ { \frac { [ x ^ { 2 } - 3 ( x - 1 ) ^ { 2 } ] } { 2 } , } & { 1 \leq x < 2 } \\ { \frac { [ x ^ { 2 } - 3 ( x - 1 ) ^ { 2 } + 3 ( x - 2 ) ^ { 2 } ] } { 2 } , } & { 2 \leq x < 3 } \\ { 0 , } & { x \notin [ 0,3 ] } \end{array} \right.$ ||  $$\empty$$ || conf 0.733
 
u09524027.png (27)
|-
| 136.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|32.]])*||  https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u0952403.png || $p ( x ) = \left\{ \begin{array} { l l } { \frac { 1 } { b - \alpha } , } & { x \in [ \alpha , b ] } \\ { 0 , } & { x \notin [ \alpha , b ] } \end{array} \right.$ ||  $$\empty$$ || conf 0.681  F 
 
u0952403.png (3)
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| 137.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|34.]]) ||  https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524030.png || $u _ { n } ( x ) = \frac { 1 } { ( n - 1 ) ! } \sum _ { k = 0 } ^ { n } ( - 1 ) ^ { k } \left( \begin{array} { l } { n } \\ { k } \end{array} \right) ( x - k ) _ { + } ^ { n - 1 }$ ||  $$\empty$$ || conf 0.569
 
u09524030.png (30)
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| 138.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|109.]]) ||  https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524034.png || $z _ { + } = \left\{ \begin{array} { l l } { z , } & { z > 0 } \\ { 0 , } & { z \leq 0 } \end{array} \right.$ ||  $$\empty$$ || conf 0.676
 
u09524034.png (34)
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| 139.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|43.]]) ||  https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u0952407.png || $F ( x ) = \left\{ \begin{array} { l l } { 0 , } & { x \leq a } \\ { \frac { x - a } { b - a } , } & { a < x \leq b } \\ { 1 , } & { x > b } \end{array} \right.$ ||  $$\empty$$ || conf 0.468
 
u0952407.png (7)
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| 140.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|47.]]) ||  https://www.encyclopediaofmath.org/legacyimages/u/u095/u095240/u09524072.png || $p ( x _ { 1 } , \ldots , x _ { n } ) = \left\{ \begin{array} { l l } { C \neq 0 , } & { x \in D } \\ { 0 , } & { x \notin D } \end{array} \right.$ ||  $$\empty$$ || conf 0.705
 
u09524072.png (72)
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==[[Unipotent group]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
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| 141.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|143.]]) ||  https://www.encyclopediaofmath.org/legacyimages/u/u095/u095410/u0954106.png || $\{ g \in \operatorname { GL } ( V ) : ( 1 - g ) ^ { n } = 0 \} , \quad n = \operatorname { dim } V$ ||  $$\empty$$ || conf 0.287
 
u0954106.png (6)
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|}
==[[Weyl module]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
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| 142.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|51.]]) ||  https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090122.png || $\operatorname { diag } ( t _ { 1 } , \ldots , t _ { n } ) \mapsto t _ { 1 } ^ { \lambda _ { 1 } } \ldots t _ { n } ^ { \lambda _ { n } } \in K$ ||  $$\empty$$ || conf 0.507
 
w120090122.png (122)
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| 143.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|54.]])*||  https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090135.png || $\chi _ { \lambda } = \sum _ { \mu \in \Lambda ( n ) } \operatorname { dim } _ { K } ( \Delta ( \lambda ) ^ { \mu } ) _ { e _ { \mu } }$ ||  $$\empty$$ || conf 0.461  F 
 
w120090135.png (135)
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| 144.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|110.]]) ||  https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090259.png || $\mathfrak { B } = \{ e _ { \pm } \alpha , h _ { \beta } : \alpha \in \Phi ^ { + } , \beta \in \Sigma \}$ ||  $$\empty$$ || conf 0.381
 
w120090259.png (259)
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| 145.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|82.]]) ||  https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w120090342.png || $\left( \begin{array} { c } { h } \\ { i } \end{array} \right) = \frac { h ( h - 1 ) \ldots ( h - i + 1 ) } { i ! }$ ||  $$\empty$$ || conf 0.487
 
w120090342.png (342)
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| 146.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|28.]])*||  https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009095.png || $\mathfrak { S } _ { \{ 1 , \ldots , \lambda _ { 1 } \} } \times \mathfrak { S } _ { \{ \lambda _ { 1 } + 1 , \ldots , \lambda _ { 1 } + \lambda _ { 2 } \} } \times$ ||  $$\empty$$ || conf 0.312  F 
 
w12009095.png (95)
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| 147.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|104.]]) ||  https://www.encyclopediaofmath.org/legacyimages/w/w120/w120090/w12009096.png || $\ldots \times \mathfrak { S } _ { \{ \lambda _ { 1 } + \ldots + \lambda _ { n - 1 } + 1 , \ldots , r \} }$ ||  $$\empty$$ || conf 0.259
 
w12009096.png (96)
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|}
==[[Witt vector]]==
{| class="wikitable" style="text-align: left; width: 1740px;"
!style=width: 3%| Nr.
!style=width: 30%| Image of png File
!style=width: 30%| $\TeX$, 1st version
!style=width: 30%| $\TeX$, corrected version
!style=width: 7%| Confidence, F?
png file 
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| 148.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|87.]])*||  https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100172.png || $\langle \alpha > < b \rangle = \langle \alpha b \rangle , \quad \langle 1 \rangle = f _ { 1 } = V _ { 1 } =$ ||  $$\empty$$ || conf 0.351  F 
 
w098100172.png (172)
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| 149.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|123.]])*||  https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100177.png || $\langle \alpha + b \rangle = \sum _ { n = 1 } ^ { \infty } V _ { n } \langle r _ { n } ( \alpha , b ) f$ ||  $$\empty$$ || conf 0.143  F 
 
w098100177.png (177)
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| 150.([[User:Maximilian Janisch/latexlist/latex/Algebraic Groups/E|102.]]) ||  https://www.encyclopediaofmath.org/legacyimages/w/w098/w098100/w098100190.png || $\sigma ( \alpha _ { 1 } , \alpha _ { 2 } , \ldots ) = ( \alpha _ { 1 } ^ { p } , \alpha _ { 2 } ^ { p } , \ldots )$ ||  $$\empty$$ || conf 0.771
 
w098100190.png (190)
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|}