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Research Article | Open Access

A note on the differential calculus of Hochschild theory for A∞-algebras

Youming Chen1, Weiguo Lyu2( ), Song Yang3
School of Science, Chongqing University of Technology, 69 Hongguang Avenue, Chongqing, MO 400054, China
School of Mathematical Sciences, Anhui University, 111 Jiulong Road, Hefei, MO 230039, China
Center for Applied Mathematics, Tianjin University, 92 Weijin Road, Tianjin, MO 300072, China
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Abstract

We show by constructing explicit homotopy operators that the Hochschild (co)homology of an A∞-algebra of Stasheff admits a differential calculus structure. As an application, we reproduce a result of Tradler which says that the Hochschild cohomology of a cyclic A∞-algebra admits a Batalin-Vilkovisky algebra structure.

Keywords

differential calculusA∞-algebracyclic A∞-algebraHochschild (co)homologyBatalin-Vilkovisky algebra

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Electronic Research Archive
Volume 30 Issue 9,
September 2022
Pages 3211-3237
DOI: 10.3934/era.2022163

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Cite this article:
Chen Y, Lyu W, Yang S. A note on the differential calculus of Hochschild theory for A∞-algebras. Electronic Research Archive, 2022, 30(9): 3211-3237. https://doi.org/10.3934/era.2022163

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Received: 28 June 2020
Revised: 21 May 2022
Accepted: 31 May 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)