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.

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• Hom-alternative algebras and Hom-Jordan algebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• Representations and module-extensions of hom 3-Lie algebras
• On split regular Hom-Lie superalgebras
• Quadratic color Hom-Lie algebras
• Cohomology of Hom-Leibniz and $n$-ary Hom-Nambu-Lie superalgebras
• Quadratic $n$-ary Hom-Nambu algebras
• Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras
• Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields
• Cohomology and Versal Deformations of Hom-Leibniz algebras