Koszul Duality for modules over Lie algebra

Details Koszul Duality for modules over Lie algebra Koszul Duality for modules over Lie algebra

2001-01-22

arxiv.org/abs/math/0101180v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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