## Duke Mathematical Journal

### Koszul duality for modules over Lie algebras

#### Abstract

Let $\mathfrak {g}$ be a reductive Lie algebra over a field of characteristic zero. Suppose that $\mathfrak {g}$ acts on a complex of vector spaces $M\sp \bullet$ by $i\sb \lambda$ and $\mathscr {L}\sb \lambda$, which satisfy the same identities that contraction and Lie derivative do for differential forms. Out of this data one defines the cohomology of the invariants and the equivariant cohomology of $M\sp \bullet$. We establish Koszul duality between them.

#### Article information

Source
Duke Math. J., Volume 112, Number 3 (2002), 511-520.

Dates
First available in Project Euclid: 18 June 2004

https://projecteuclid.org/euclid.dmj/1087575185

Digital Object Identifier
doi:10.1215/S0012-9074-02-11234-4

Mathematical Reviews number (MathSciNet)
MR1896472

Zentralblatt MATH identifier
1014.17018

Subjects
Primary: 17B55: Homological methods in Lie (super)algebras

#### Citation

Maszczyk, Tomasz; Weber, Andrzej. Koszul duality for modules over Lie algebras. Duke Math. J. 112 (2002), no. 3, 511--520. doi:10.1215/S0012-9074-02-11234-4. https://projecteuclid.org/euclid.dmj/1087575185

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