Cyclic cohomology of Lie algebras

Details Cyclic cohomology of Lie algebras Cyclic cohomology of Lie algebras

2011-08-13

arxiv.org/abs/1108.2806v1

Mathematics

Quantum Algebra

33 pages

Scientific paper

In this paper we aim to understand the category of stable-Yetter-Drinfeld modules over enveloping algebra of Lie algebras. To do so, we need to define such modules over Lie algebras. These two categories are shown to be isomorphic. A mixed complex is defined for a given Lie algebra and a stable-Yetter-Drinfeld module over it. This complex is quasi-isomorphic to the Hopf cyclic complex of the enveloping algebra of the Lie algebra with coefficients in the corresponding module. It is shown 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.

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