Lie algebra cohomology

In mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was defined by Chevalleyand Eilenberg (1948) in order to give an algebraic construction of the cohomology of the underlying topological spaces of compact Lie groups. In the paper above, a specific chain complex, called the Koszul complex, is defined for a module over a Lie algebra, and its cohomology is taken in the normal sense.