Structure and classification of Hom-associative algebras

Ahmed Zahari; Abdenacer Makhlouf

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arXiv · 1906.04969

Structure and classification of Hom-associative algebras

Ahmed Zahari·Abdenacer Makhlouf

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Abstract

The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra to simple Hom-associative algebras. We provide a classification of $n$-dimensional Hom-associative algebras for $n\leq3$. Then study their derivations and compute small Hom-Type Hochschild cohomology groups. Furthermore, we discuss their irreducible components.

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Ahmed Zahari, Abdenacer Makhlouf. 2019-06-12. Structure and classification of Hom-associative algebras. https://arxiv.org/abs/1906.04969

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