Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras

Details Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras

2009-06-09

arxiv.org/abs/0906.1668v2

Mathematics

Rings and Algebras

Scientific paper

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 $\Gamma$-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 $\mathbb{Z}_2$-graded version of a Hartwig-Larsson-Silvestrov Theorem which leads us to a construction of a q-deformed Witt superalgebra.

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