Non-degenerate Killing forms on Hom-Lie superalgebras

Abstract

In this paper we investigate some important basic properties of simple Hom-Lie superalgebras and show that a Hom-Lie superalgebra does not have any left or right nontrivial ideals. Moreover, we classify invariant bilinear forms on a given simple Hom-Lie superalgebra. Then we study the Killing forms on a Hom-Lie algebra which are examples of the invariant bilinear forms. Making use of the Killing forms, we find conditions for a Hom-Lie superalgebra to be classical. Furthermore, we check the conditions in which the Killing form of a Hom-Lie superalgebra is non-degenerate.

typos corrected, references added

References in corpus (6)

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• Quasi-Lie structure of twisted derivations of Laurent polynomials
• Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras
• Generalized Derivations of Hom-Lie Superalgebras
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