Hom-Lie superalgebras and Hom-Lie admissible superalgebras

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 Z2-graded version of a Hartwig–Larsson–Silvestrov Theorem which leads us to a construction of a q-deformed Witt superalgebra.