Structure and classification of Hom-associative algebras

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 $n\le 3$. Then study their derivations and compute small Hom-Type Hochschild cohomology groups. Furthermore, we discuss their irreducible components.

References in corpus (2)

• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras