mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices...
28 KB (4,308 words) - 17:20, 8 November 2023
mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an...
61 KB (10,442 words) - 17:43, 23 May 2024
mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero...
41 KB (5,731 words) - 17:17, 10 April 2024
by conjugation. The adjoint representation can be defined for linear algebraic groups over arbitrary fields. Let G be a Lie group, and let Ψ : G → Aut...
21 KB (3,516 words) - 06:10, 20 February 2024
representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization...
22 KB (3,339 words) - 16:22, 15 May 2024
include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which...
55 KB (7,169 words) - 20:10, 17 May 2024
of the corresponding 'infinitesimal' representations of Lie algebras. A complex representation of a group is an action by a group on a finite-dimensional...
34 KB (5,242 words) - 21:39, 18 September 2023
In mathematics, the special linear Lie algebra of order n over a field F {\displaystyle F} , denoted s l n F {\displaystyle {\mathfrak {sl}}_{n}F} or...
11 KB (1,930 words) - 23:24, 10 May 2024
Equivalently, a representation of L is a Z2-graded representation of the universal enveloping algebra of L which respects the third equation above. A * Lie superalgebra...
3 KB (420 words) - 00:48, 29 March 2024
In algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals. The classification of real simple Lie algebras...
3 KB (538 words) - 09:30, 11 October 2023