Koszul Duality for modules over Lie algebra

Abstract

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 $L_{\lambda }$, which satisfy the identities as contraction and Lie derivative do for smooth differential forms. Out of this data one defines cohomology of the invariants and equivariant cohomology of $M$. We establish Koszul duality between each other.

11 pages, LaTeX, final version: to appear in Duke Math. J