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arXiv · 2009.12266

Noncommutative differential calculus on (co)homology of hom-associative algebras

Apurba Das
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Abstract

A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-associative algebra $A$ carries a Gerstenhaber structure. In this short paper, we show that this Gerstenhaber structure together with certain operations on the Hochschild homology of $A$ makes a noncommutative differential calculus. As an application, we obtain a Batalin-Vilkovisky algebra structure on the Hochschild cohomology of a regular unital symmetric hom-associative algebra.

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Apurba Das. 2020-09-25. Noncommutative differential calculus on (co)homology of hom-associative algebras. https://arxiv.org/abs/2009.12266

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