Gerstenhaber algebra structure on the cohomology of a hom-associative algebra

Apurba Das

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arXiv · 1805.01207

Gerstenhaber algebra structure on the cohomology of a hom-associative algebra

Apurba Das

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Abstract

A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. In this paper, we define a cup product on the cohomology of a hom-associative algebra. We show that the cup product together with the degree $-1$ graded Lie bracket (which controls the deformation of the hom-associative algebra structure) on the cohomology forms a Gerstenhaber algebra. This generalizes a classical fact that the Hochschild cohomology of an associative algebra carries a Gerstenhaber algebra structure.

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Apurba Das. 2018-05-03. Gerstenhaber algebra structure on the cohomology of a hom-associative algebra. https://arxiv.org/abs/1805.01207

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