Finite-dimensional simple Hom-alternative algebras are exactly twists of semi-simple alternative algebras by automorphisms, and their bimodules with invertible module twist are equivalent to bimodules of the untwisted algebra.
Structure and classification of Hom-associative algebras
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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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Structures and bimodules of simple Hom-alternative algebras
Finite-dimensional simple Hom-alternative algebras are exactly twists of semi-simple alternative algebras by automorphisms, and their bimodules with invertible module twist are equivalent to bimodules of the untwisted algebra.