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 $\Gamma$-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.

References in corpus (6)

• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Quasi-Deformations of sl_2(\F) using twisted derivations
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Cited by in corpus (7)

• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-alternative algebras and Hom-Jordan algebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• On split regular Hom-Lie superalgebras
• Quadratic color Hom-Lie algebras
• Cohomology of Hom-Leibniz and $n$-ary Hom-Nambu-Lie superalgebras
• Cohomology and Versal Deformations of Hom-Leibniz algebras