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Mathematics > Rings and Algebras
Title: Non-degenerate Killing forms on Hom-Lie superalgebras
(Submitted on 5 Oct 2020 (v1), last revised 6 Oct 2020 (this version, v2))
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.
Submission history
From: Sergei Silvestrov [view email][v1] Mon, 5 Oct 2020 04:57:21 GMT (16kb)
[v2] Tue, 6 Oct 2020 01:22:51 GMT (16kb)
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