View source for User:Maximilian Janisch/latexlist/Algebraic Groups/Anisotropic kernel

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The subgroup $\Omega$ of a semi-simple [[Algebraic group|algebraic group]] $k$, defined over a field $k$, which is the commutator subgroup of the centralizer of a maximal $k$-split torus $S \subset G$; $D = [ Z _ { G } ( S ) , Z _ { G } ( S ) ]$. The anisotropic kernel $\Omega$ is a semi-simple [[Anisotropic group|anisotropic group]] defined over $k$; $D = \operatorname { rank } G -$. The concept of the anisotropic kernel plays an important role in the study of the $k$-structure of $k$ [[#References|[1]]]. If $D = G$, i.e. if $G = 0$, then $k$ is anisotropic over $k$; if $D = ( e )$, the group $k$ is called quasi-split over $k$.

====References====
<table><tr><td valign="top">[1]</td> <td valign="top">  J. Tits,   "Classification of algebraic simple groups" , ''Algebraic Groups and Discontinuous Subgroups'' , ''Proc. Symp. Pure Math.'' , '''9''' , Amer. Math. Soc.  (1966)  pp. 33–62    {{MR|}} {{ZBL|}} </td></tr><tr><td valign="top">[2]</td> <td valign="top">  A. Borel,   J. Tits,   "Groupes réductifs"  ''Publ. Math. IHES'' , '''27'''  (1965)  pp. 55–150  {{MR|0207712}} {{ZBL|0145.17402}} </td></tr></table>