Some characterizations of Hom-Leibniz algebras

Abstract

Some basic properties of Hom-Leibniz algebras are found. These properties are the Hom-analogue of corresponding well-known properties of Leibniz algebras. Considering the Hom-Akivis algebra associated to a given Hom-Leibniz algebra, it is observed that the Hom-Akivis identity leads to an additional property of Hom-Leibniz algebras, which in turn gives a necessary and sufficient condition for Hom-Lie admissibility of Hom-Leibniz algebras. A necessary and sufficient condition for Hom-power associativity of Hom-Leibniz algebras is also found.

LaTeX2e, no figure

References in corpus (5)

• Hom-algebras and homology
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-power associative algebras
• Engel subalgebras of Leibniz algebras
• Hom-Akivis algebras

Cited by in corpus (2)

• Hom-Lie-Yamaguti structures on Hom-Leibniz algebras
• Color Hom-Akivis algebras, Color Hom-Leibniz algebras and Modules over Color Hom-Leibniz algebras