June 5, 2024Open Access

On the Schur multiplier of nilpotent Lie superalgebra

ASAfsaneh ShamsakiFerdowsi University of Mashhad PNPeyman NiroomandDamghan University

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Abstract

Let L be an (m n) -dimensional nilpotent Lie superalgebra where m + n 4 and n 1. This paper classifies such nilpotent Lie superalgebras L with a derived subsuperalgebra of dimension m+n-2 such that (L) = m + 2n - 2 - M (L), where (L) \0, 1, 2\ and M (L) denotes the Schur multiplier of L. Furthermore, we show that all these superalgebras are capable.

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Shamsaki et al. (Wed,) studied this question.

synapsesocial.com/papers/68e660e5b6db6435875ef587 https://doi.org/https://doi.org/10.48550/arxiv.2406.03573

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1Classification of Finite Dimensional Nilpotent Lie Superalgebras by their Multipliers2021
2Upper bounds on the dimension of the Schur $\mathsf{Lie}$-multiplier of $\mathsf{Lie}$-nilpotent Leibniz $n$-algebras2024
3On the Schur Multiplier of n-Lie Algebras2017
4Capability of nilpotent Lie superalgebras of small dimension2024
5The Schur Multiplier of Some Finite Multiplicative Lie Algebras2024

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