Batalin-Vilkovisky Algebras and Cyclic Cohomology of Hopf Algebras

Abstract

We show that the Connes-Moscovici cyclic cohomology of a Hopf algebra equipped with a character has a Lie bracket of degree -2.More generally, we show that a "cyclic operad with multiplication" is a cocyclic module whose cohomology is a Batalin-Vilkovisky algebra and whose cyclic cohomology is a graded Lie algebra of degree -2.This explain why the Hochschild cohomology algebra of a symmetric algebra is a Batalin-Vilkovisky algebra.