Batalin-Vilkovisky algebras and cyclic cohomology of Hopf algebras

2003/11/17 by Luc Menichi, Menichi, Luc · 1 citation
Mathematics · #16E40 #16W30 #18D50 #19D55 #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AT #math.QA #msc:16E40 #msc:16W30 #msc:18D50 #msc:19D55

paper · pdf · doi:10.48550/arxiv.math/0311276

19 pages

arxiv created 2003/11/17 · arxiv updated 2009/12/01

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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• Brace B_∞ algebras associated with Hopf algebroids

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