Cyclic cohomology of Lie algebras

Abstract

We define and completely determine the category of Yetter-Drinfeld modules over Lie algebras. We prove a one to one correspondence between Yetter-Drinfeld modules over a Lie algebra and those over the universal enveloping algebra of the Lie algebra. We associate a mixed complex to a Lie algebra and a stable-Yetter-Drinfeld module over it. We show that the (truncated) Weil algebra, the Weil algebra with generalized coefficients defined by Alekseev-Meinrenken, and the perturbed Koszul complex introduced by Kumar-Vergne are examples of such a mixed complex.