Paradigm of Nonassociative Hom-algebras and Hom-superalgebras

Details Paradigm of Nonassociative Hom-algebras and Hom-superalgebras Paradigm of Nonassociative Hom-algebras and Hom-superalgebras

2010-01-24

arxiv.org/abs/1001.4240v1

Mathematics

Rings and Algebras

Dedicated to Amine Kaidi on his 60th birthday

Scientific paper

The aim of this paper is to give a survey of nonassociative Hom-algebra and Hom-superalgebra structures. The main feature of these algebras is that the identities defining the structures are twisted by homomorphisms. We discuss Hom-associative algebras, Hom-Flexible algebras, Hom-Lie algebras, $G$-hom-associative algebras, Hom-Poisson algebras, Hom-alternative algebras and Hom-Jordan algebras and $\mathbb{Z}_2$-graded versions. We give an overview of the development of Hom-algebras structures which have been intensively investigated recently.

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