An Alternate Approach to the Lie Bracket on Hochschild Cohomology

2014/05/30 by Cris Negron, Negron, Cris, Sarah Witherspoon +1
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.KT #math.QA #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1406.0036

20 pages, updated introduction

arxiv created 2015/03/16 · arxiv updated 2015/03/18

Abstract

We define Gerstenhaber's graded Lie bracket directly on complexes other than the bar complex, under some conditions. The Koszul complex of a Koszul algebra in particular satisfies our conditions. As examples we recover the Schouten-Nijenhuis bracket for a polynomial ring and the Gerstenhaber bracket for a group algebra of a cyclic group of prime order.

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