Algebra whose powers eventually vanish.

In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket.

In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras.

In algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals.

In mathematics, a Lie algebra is solvable if its derived series terminates in the zero subalgebra.

In the 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 (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator.

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

In mathematics, the special linear Lie algebra of order over a field , denoted or , is the Lie algebra of all the matrices (with entries in ) with trace zero and with the Lie bracket given by the commutator.