# Perfect Lie algebra

From Groupprops

*This article defines a property for a Lie algebra*

ANALOGY: This is an analogue in Lie algebra of a property encountered in group. Specifically, it is a Lie algebra property analogous to the group property: perfect group

View other analogues of perfect group | View other analogues in Lie algebras of group properties (OR, View as a tabulated list)

## Definition

A Lie algebra is said to be **perfect** if it equals its own commutator ideal. In other words, a Lie algebra is said to be perfect if every element of the Lie algebra is in the ideal generated by commutators.

Also see perfect Lie ring.