A note on the differential calculus of Hochschild theory for $ A_{\infty} $-algebras-Reference-Cited by-同舟云学术

A note on the differential calculus of Hochschild theory for $ A_{\infty} $-algebras

Published:2022 Issue:9 Volume:30 Page:3211-3237
ISSN:2688-1594
Container-title:Electronic Research Archive
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Short-container-title:era

Author:

Chen Youming¹,Lyu Weiguo²,Yang Song³

Affiliation:

1. School of Science, Chongqing University of Technology, 69 Hongguang Avenue, Chongqing, MO 400054, China

2. School of Mathematical Sciences, Anhui University, 111 Jiulong Road, Hefei, MO 230039, China

3. Center for Applied Mathematics, Tianjin University, 92 Weijin Road, Tianjin, MO 300072, China

Abstract

<abstract><p>We show by constructing explicit homotopy operators that the Hochschild (co)homology of an $ A_{\infty} $-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_\infty $-algebra admits a Batalin-Vilkovisky algebra structure.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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