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Batalin-Vilkovisky algebras and cyclic cohomology of Hopf algebras

Luc Menichi
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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.

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Luc Menichi. 2003-11-17. Batalin-Vilkovisky algebras and cyclic cohomology of Hopf algebras. https://arxiv.org/abs/math/0311276

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