
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 -Hom-associative algebras are constructed as deformations of -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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
