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arXiv · 2008.07941

Z-graded Hom-Lie Superalgebras

M. R. Farhangdoost·A. R. Attari Polsangi
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Abstract

In this paper we introduce the notions of Z-graded hom-Lie superalgebras and we show that there is a maximal (resp., minimal) Z-graded hom-Lie superalgebra for a given local hom-Lie superalgebra. Morever, we introduce the invariant bilinear forms on a Z-graded hom-Lie superalgebra and we prove that a consistent supersymmetric {\alpha}-invariant form on the local part can be extended uniquely to a bilinear form with the same property on the whole Z-graded hom-Lie superalgebra. Furthermore, we check the condition in which the Z-graded hom-Lie superalgebra is simple.

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M. R. Farhangdoost, A. R. Attari Polsangi. 2020-08-18. Z-graded Hom-Lie Superalgebras. https://arxiv.org/abs/2008.07941

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