## 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.