Paradigm of Nonassociative Hom-algebras and Hom-superalgebras

By Abdenacer Makhlouf. 2010

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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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ba1c9ac35506d19ef64ff74c8a8e36c593f5f167