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...

mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an...

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...

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...

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...

include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which...

mathematics, the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory...

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...

of the corresponding 'infinitesimal' representations of Lie algebras. A complex representation of a group is an action by a group on a finite-dimensional...

Élie Cartan in his doctoral thesis. It controls the representation theory of a semi-simple Lie algebra g {\displaystyle {\mathfrak {g}}} over a field of...