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

Electronic Research Archive（2022）

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摘要

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.

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关键词

differential calculus,$ a_{\infty} $-algebra,cyclic $ a_{\infty} $-algebra,hochschild (co)homology,batalin-vilkovisky algebra

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