Gerstenhaber Bracket on the Hochschild Cohomology via An Arbitrary Resolution
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Publication:4966895
DOI10.1017/S0013091518000901zbMATH Open1461.16005arXiv1610.05741OpenAlexW2963864663MaRDI QIDQ4966895
Author name not available (Why is that?)
Publication date: 28 June 2019
Published in: (Search for Journal in Brave)
Abstract: We prove formulas of different types that allow to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Using one of these formulas, we give a new short proof of the derived invariance of the Gerstenhaber algebra structure on Hochschild cohomology. Also we give some new formulas for the Connes' differential on the Hochschild homology that lead to formulas for BV differential on the Hochschild cohomology in the case of symmetric algebras. Finally, we use one of the obtained formulas to get a full description of the BV structure and, correspondingly, the Gerstenhaber algebra structure on the Hochschild cohomology of a class of symmetric algebras.
Full work available at URL: https://arxiv.org/abs/1610.05741
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