Structure and classification of Hom-associative algebras

Authors

  • Abdenacer Makhlouf Université de Haute Alsace, IRIMAS-département de Mathématiques, 6, rue des Frères Lumière F-68200 Mulhouse, France https://orcid.org/0000-0002-5329-487X
  • Ahmed Zahari Université de Haute Alsace, IRIMAS-département de Mathématiques, 6, rue des Frères Lumière F-68200 Mulhouse, France

DOI:

https://doi.org/10.12697/ACUTM.2020.24.06

Keywords:

Hom-associative algebra, simple Hom-associative algebra, classification, cohomology, irreducible component

Abstract

The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We characterize multiplicative simple Hom-associative algebras and give some examples deforming the 2 × 2-matrix algebra to simple Hom-associative algebras. We provide a classification of n-dimensional Hom-associative algebras for n ≤ 3. Then we study irreducible components using deformation theory.

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Published

2020-09-23

Issue

Vol. 24 No. 1 (2020)

Section

Articles

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