Gerstenhaber bracket on the Hochschild cohomology via an arbitrary\n resolution

2016/10/18 by Yury Volkov, Volkov, Yury · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1610.05741

Abstract

We prove formulas of different types that allow to calculate the Gerstenhaber\nbracket on the Hochschild cohomology of an algebra using some arbitrary\nprojective bimodule resolution for it. Using one of these formulas, we give a\nnew short proof of the derived invariance of the Gerstenhaber algebra structure\non Hochschild cohomology. Also we give some new formulas for the Connes'\ndifferential on the Hochschild homology that lead to formulas for BV\ndifferential on the Hochschild cohomology in the case of symmetric algebras.\nFinally, we use one of the obtained formulas to get a full description of the\nBV structure and, correspondingly, the Gerstenhaber algebra structure on the\nHochschild cohomology of a class of symmetric algebras.\n

Cited by

• Corings, their dual rings and relative (co)Hochschild cohomology
• Comultiplicative map on projective resolution for a family of algebras one of which is cluster-tilted type D4

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