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

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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. A direct verification shows that this cup product together with the degree \(-1\) graded Lie bracket (which controls the deformation of the hom-associative algebra structure) on the cohomology makes it a Gerstenhaber algebra.

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Acknowledgements

The author would like to thank the referee for his/her valuable comments on an earlier version of the manuscript. The research has been carried out when the author was a research fellow at the Indian Statistical Institute, Kolkata, India. He wishes to thank the Institute for their support.

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  1. Apurba Das

    Present address: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208 016, India

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    Communicating Editor: Parameswaran Sankaran

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    Das, A. Gerstenhaber algebra structure on the cohomology of a hom-associative algebra. Proc Math Sci 130, 20 (2020). https://doi.org/10.1007/s12044-019-0543-3

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    • DOI: https://doi.org/10.1007/s12044-019-0543-3

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