...he rotation of a tangle by the angle $\pi /n$ and $*$ denotes (horizontal) composition of tangles.
...of knots and links" J. Leech (ed.) , ''Computational Problems in Abstract Algebra'' , Pergamon Press (1969) pp. 329–358</td></tr><tr><td valign="top">[a2
2 KB (401 words) - 16:58, 1 July 2020
$#C+1 = 55 : ~/encyclopedia/old_files/data/B110/B.1100750 Boolean algebra with operators
An operator on a Boolean algebra $ \mathbf B $
8 KB (1,220 words) - 19:12, 11 December 2020
...ncyclopedia/old_files/data/R081/R.0801430 Representation of an associative algebra
A homomorphism of the algebra $ A $
22 KB (3,137 words) - 20:01, 15 March 2023
The Cartan matrix of a finite-dimensional semi-simple Lie algebra $\def\fg{\mathfrak{g}}\fg$ over an algebraically closed field $k$ of charac
...a transformation induced by permutation of the indices. A semi-simple Lie algebra is simple if and only if its Cartan matrix is indecomposable, that is, not
6 KB (1,055 words) - 08:14, 22 May 2012
...[tilting module]] over a finite-dimensional hereditary algebra (cf. also [[Algebra]]; [[Endomorphism]]).
...e-dimensional hereditary $K$-algebra, $K$ some field, for example the path-algebra of some finite [[quiver]] without oriented cycles. A finite-dimensional $H$
8 KB (1,215 words) - 19:50, 24 December 2023
...truction that first appeared in set theory, and then became widely used in algebra, topology and other areas of mathematics. An important special case of an i
with the obvious law of composition. In an arbitrary category $ \mathfrak K $,
7 KB (1,089 words) - 22:12, 5 June 2020
The naturally defined composition of local homomorphisms is also a local homomorphism. Local homomorphisms $
...s the correspondence between the local Lie group and its [[Lie algebra|Lie algebra]]. Namely, let $ G $
10 KB (1,553 words) - 22:16, 5 June 2020
1) each of $E$ and $M$ is closed under composition with isomorphisms;
...$E$ of morphisms and a family $\mathfrak{M}$ of sources, each closed under composition with isomorphisms, such that each source $\mathcal{S}$ in $\frak A$ has a f
11 KB (1,634 words) - 01:54, 13 February 2024
...[[Differentiable manifold|differentiable manifold]], and let $F(M)$ be the algebra of smooth real-valued functions on it. A tangent vector to $M$ at $m\in M$
...psto g\alpha$. For a tangent vector $v:F(M)\rightarrow \mathbb{R}$ at $m$, composition with $\alpha^*$ gives an $\mathbb{R}$-linear mapping $v\alpha^*:F(N)\righta
8 KB (1,509 words) - 05:24, 22 May 2017
...$\mathcal{C} ( C , C ^ { \prime } )$ (cf. also [[Free group|Free group]]). Composition is defined in the unique way so as to be bilinear and to make the inclusion
...}$ equipped with a $K$-module structure on each hom-set in such a way that composition induces a $K$-module homomorphism. If $K = \mathcal{Z}$, a $\mathcal Z$-cat
9 KB (1,283 words) - 20:55, 8 February 2024
...s a [[Ringoid|ringoid]] over a group, i.e. a [[Universal algebra|universal algebra]] in which an associative multiplication and addition exist; a near-ring is
...$M_S(\Gamma)$ are defined pointwise and multiplication in $M_S(\Gamma)$ is composition of mappings. A near-ring $M_S(\Gamma)$ is an analogue of a ring of matrices
5 KB (767 words) - 11:23, 27 October 2014
under natural composition. Factor sets corresponding to a semi-direct product form a subgroup $ B _
...extensions is one of the cornerstones of [[Homological algebra|homological algebra]].
6 KB (917 words) - 20:29, 17 January 2024
...othety with coefficient $k$ or $-k$. Any similarity can be considered as a composition of a motion $D$ and some homothety $\Gamma$ with a positive coefficient.
...e><TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Artin, "Geometric algebra" , Interscience (1957) pp. Chapt. II</TD></TR><TR><TD valign="top">[a2]</
3 KB (509 words) - 14:19, 12 April 2014
$#C+1 = 261 : ~/encyclopedia/old_files/data/L058/L.0508360 Lie\AAhadmissible algebra
...the defining identities for standard algebras [[#References|[a1]]]. For an algebra $ \mathfrak A $
22 KB (3,154 words) - 19:10, 26 March 2023
An algebra over a field for which certain polynomial identities are true.
be an associative algebra (cf. [[Associative rings and algebras|Associative rings and algebras]]) ove
15 KB (2,252 words) - 08:04, 6 June 2020
$#C+1 = 107 : ~/encyclopedia/old_files/data/M110/M.1100020 Magari algebra,
''diagonalizable algebra''
13 KB (1,762 words) - 11:49, 12 January 2021
...operators on a Hilbert space (a uniformly closed [[C*-algebra|$C ^ { * }$-algebra]]). Such algebras are closely connected to important fields of geometric an
...$ with continuous symbol $f$ is not commutative, but defines a $C ^ { * }$-algebra extension
8 KB (1,186 words) - 16:46, 1 July 2020
For the [[Topological algebra|topological algebra]] $A ^ { - \infty } = \cup _ { p > 0 } L _ { a } ^ { p }$, B. Korenblum has
There also are well-developed theories of Toeplitz, Hankel, and composition operators on Bergman spaces, and work on Bergman spaces on domains in $\mat
12 KB (1,859 words) - 14:41, 27 January 2024
...s were introduced as the basis for an abstract construction of homological algebra [[#References|[4]]]. A category $ \mathfrak A $
These constitute the basis for the development of homological algebra.
10 KB (1,515 words) - 18:19, 31 March 2020
...C_1$ and $C_2$ over an associative commutative ring $A$ with a unit is the algebra $C_1 \tensor_A C_2$ over $A$ which is obtained by introducing on the tensor
...phic to $C_1$ and $C_2$ and commute elementwise. Conversely, let $C$ be an algebra with a unit over the field $A$, and let $C_1$ and $C_2$ be subalgebras of i
11 KB (1,992 words) - 03:52, 23 July 2018