##
Koszul Duality for modules over Lie algebra

**Tomasz Maszczyk, Andrzej Weber**

11 pages

Let $\g$ be a reductive Lie algebra over a field of characteristic
zero. Suppose $\g$ acts on a complex of vector spaces $\M$ by $i_\lambda$
and $\Ll_\lambda$, which satisfy the identities as contraction and Lie
derivative do for differential forms. Out of this data one defines
cohomology of the invariants and equivariant cohomology of $\M$. We
establish Koszul duality between each other.