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arXiv · 1806.01169

$\alpha$-type Hochschild cohomology of Hom-associative algebras and Hom-bialgebras

Benedikt Hurle·Abdenacer Makhlouf
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Abstract

In this paper we define a new cohomology for multiplicative Hom-associative algebras, which generalize Hochschild cohomology and fits with deformations of Hom-associative algebras including the structure map $\alpha$. It is a generalization of the known Hochschild-type cohomology for Hom-associative algebras defined by Amar, Ejbehi and Makhlouf. Moreover, we provide various observations and similarly a new cohomology of Hom-bialgebras extending the Gerstenhaber-Schack cohomology for Hom-bialgebras given by Dekkar and Makhlouf.

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Benedikt Hurle, Abdenacer Makhlouf. 2018-06-04. $\alpha$-type Hochschild cohomology of Hom-associative algebras and Hom-bialgebras. https://arxiv.org/abs/1806.01169

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