Super-biderivations and post-Lie superalgebras on some Lie superalgebras

Dilxat, Munayim; Gao, Shoulan; Liu, Dong

doi:10.48550/arxiv.2206.05925

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2023

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“…Meanwhile, applications for and results on biderivations and super-biderivations of simple Lie superalgebras arose in [25]. For example, based on the theory related to super-biderivations, the authors obtained commutative post-Lie superalgebra structures [26]. The skew-symmetric super-biderivations of generalized Witt Lie superalgebra W(m, n; t) were proved to be inner in [27].…”

Section: Introductionmentioning

confidence: 99%

A Note on Finite Dimensional Odd Contact Lie Superalgebra in Prime Characteristic

Xu,

Wang

2023

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Over a field of characteristic p>3, let KO(n,n+1;t̲) denote the odd contact Lie superalgebra. In this paper, the super-biderivations of odd Contact Lie superalgebra KO(n,n+1;t̲) are studied. Let TKO be a torus of KO(n,n+1;t̲), which is an abelian subalgebra of KO(n,n+1;t̲). By applying the weight space decomposition approach of KO(n,n+1;t̲) with respect to TKO, we show that all skew-symmetric super-biderivations of KO(n,n+1;t̲) are inner super-biderivations.

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Section: Introductionmentioning

confidence: 99%