Gerstenhaber bracket on the Hochschild cohomology via an arbitrary resolution
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.
Keywords
Cite
@article{arxiv.1610.05741,
title = {Gerstenhaber bracket on the Hochschild cohomology via an arbitrary resolution},
author = {Yury Volkov},
journal= {arXiv preprint arXiv:1610.05741},
year = {2018}
}
Comments
The paper is accepted to Proceedings of the Edinburgh Mathematical Society. The main difference between the second and the first version is a new short proof of the derived invariance of the Gerstenhaber algebra structure on Hochschild cohomology