Hom-algebras and homology

TL;DR

This paper introduces Hom-algebras as deformations of classical algebras via endomorphisms and develops a homology theory for Hom-Lie algebras, expanding the algebraic framework.

Contribution

It constructs G-Hom-associative algebras as deformations and develops Chevalley-Eilenberg type homology for Hom-Lie algebras, providing new tools in algebraic deformation theory.

Findings

Hom-associative and Hom-Lie algebras obtained as deformations

Chevalley-Eilenberg type homology constructed for Hom-Lie algebras

Framework extends classical algebraic structures with endomorphism-based deformations

Abstract

Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as deformations of associative and Lie algebras, respectively, along algebra endomorphisms. Chevalley-Eilenberg type homology for Hom-Lie algebras are also constructed.