Research ArticleNo Access

Homotopy liftings and Hochschild cohomology of some twisted tensor products

Pablo S. Ocal

UCLA Mathematics Department, Los Angeles, CA, 90095-1555, USA

E-mail Address: [email protected]

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Tolulope Oke

Department of Mathematics and Statistics, Wake Forest University, 383 Manchester Hall, Winston-Salem, NC 27101, USA

E-mail Address: [email protected]

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, and

Sarah Witherspoon

Department of Mathematics, Texas A&M University, College Station, Texas 77843, USA

E-mail Address: [email protected]

corresponding author.

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https://doi.org/10.1142/S0219498822502383Cited by:1 (Source: Crossref)

Abstract

The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We present new proofs of these isomorphisms, using Volkov’s homotopy liftings that were introduced for handling Gerstenhaber brackets expressed on arbitrary bimodule resolutions. Our results illustrate the utility of homotopy liftings for theoretical purposes.

Communicated by D. Hebera

Keywords:

AMSC: 16E40

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