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Batalin-Vilkovisky Algebras and Cyclic Cohomology of Hopf Algebras
Authors:Luc Menichi
Institution:(1) Associee Au CNRS, Faculte des Sciences, Universite drsquo Angers, UMR 6093, 2 Boulevard Lavoisier, 49045 Angers, France
Abstract:We show that the Connes–Moscovici negative cyclic cohomology of a Hopf algebra equipped with a character has a Lie bracket of degree -2. More generally, we show that a lsquolsquocyclic operad with multiplicationrdquo is a cocyclic module whose simplicial cohomology is a Batalin–Vilkovisky algebra and whose negative cyclic cohomology is a graded Lie algebra of degree -2. This generalizes the fact that the Hochschild cohomology algebra of a symmetric algebra is a Batalin–Vilkovisky algebra.
Keywords:Batalin–  Vilkovisky algebra  cyclic cohomology  cyclic operad  Hopf algebra  Hochschild cohomology
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