Chevalley-Eilenberg complex

Definition

Suppose $L$ is a Lie algebra over a base field $K$. The Chevalley-Eilenberg complex of $L$, also called the standard complex of $L$, is a particular chain complex of $L$-modules that can serve as a projective resolution of $K$ as a trivial $L$-module.

It can be thought of as a kind of Lie algebra analogue of the bar resolution for groups.