Restricted Hom-Lie Superalgebras

Abstract

The aim of this paper is to introduce the notion of restricted Hom-Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to obtain restricted Hom-Lie superalgebras from the classical restricted Lie superalgebras along with algebra endomorphisms. Homomorphisms relations between restricted Hom-Lie superalgebras are defined and studied. Also, we obtain some properties of p-maps and restrictable Hom-Lie superalgebras.

Key words and phrases. Hom-Lie superalgebra; Restricted Hom-Lie superalgebra; p-map; Restrictable Hom-Lie superalgebra; Morphism.

2000 Mathematics Subject Classification. 17A70, 17A60, 17B75, 17B56.