Hom-Lie superalgebras and Hom-Lie admissible superalgebras

Abstract

The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of Γ -graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one parameter family of Hom-Lie superalgebras deforming the orthosymplectic Lie superalgebra. Also, we prove a Z 2 -graded version of a Hartwig–Larsson–Silvestrov Theorem which leads us to a construction of a q -deformed Witt superalgebra.