Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras

Abstract

Hom-alternative, Hom-Malcev and Hom-Jordan superalgebras are ${\mathbb{Z}}_2$-graded generalizations of Hom-alternative, Hom-Malcev and Hom-Jordan algebras, which are Hom-type generalizations of alternative, Malcev and Jordan algebras. In this paper we prove that Hom-alternative superalgebras are Hom-Malcev-admissible and are also Hom-Jordan-admissible. Home-type generalizations of some well known identities in alternative superalgebras, including the ${\mathbb{Z}}_2$-graded Bruck-Kleinfled function are obtained.

arXiv admin note: substantial text overlap with arXiv:1002.3944 by other authors

References in corpus (4)

• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• On Hom-algebra structures