The classical Lie algebras are finite-dimensional Lie algebras over a field which can be classified into four types A n {\displaystyle A_{n}} , B n {\displaystyle...

y]=xy-yx} . Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds: every Lie group gives rise to a Lie algebra, which...

{sp}}_{2n}\mathbb {C} } (classical Lie algebras) or one of the five exceptional Lie algebras. To each finite-dimensional complex semisimple Lie algebra g {\displaystyle...

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...

are the simple Lie algebras of compact groups? It turns out that they mostly fall into four infinite families, the "classical Lie algebras" An, Bn, Cn and...

Lie groups are exactly the Lie groups whose Lie algebras are semisimple Lie algebras. The Lie algebra of a simple Lie group is a simple Lie algebra....

F4 : E6 : E7 : E8 : In contrast, simple Lie algebras that are not exceptional are called classical Lie algebras (there are infinitely many of them). There...

theory of semisimple Lie algebras. For classical Lie algebras there is a more explicit construction. Let g0 be a real Lie algebra of matrices over R that...

Lie groups, Lie algebras and their representation theory, a Lie algebra extension e is an enlargement of a given Lie algebra g by another Lie algebra...

operation. Most naturally occurring Lie algebras in characteristic p come with this structure, because the Lie algebra of a group scheme over a field of...