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Hom-algebras and homology. (English) Zbl 1252.17002
Summary: 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.

MSC:
17A30 Nonassociative algebras satisfying other identities
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
17B55 Homological methods in Lie (super)algebras
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