Paradigm of Nonassociative Hom-algebras and Hom-superalgebras

Abstract

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.

Dedicated to Amine Kaidi on his 60th birthday

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Cited by in corpus (5)

• A twisted generalization of Lie-Yamaguti algebras
• Some characterizations of Hom-Leibniz algebras
• Extensions of hom-Lie color algebras
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras
• Enveloping algebras of color hom-Lie algebras