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arXiv · 1810.09129

Classification of finite dimensional nilpotent Lie superalgebras by their multiplier

Saudamini Nayak
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Abstract

Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $s(L) = \frac{1}{2}[(m + n - 1)(m + n -2)]+ n+ 1 - \dim \mathcal{M}(L)$, where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Here $s(L)\geq 0$ and the structure of all non-abelian nilpotent Lie superalgebras with $s(L)=0$ is known((\cite{Nayak2019}). This paper is devoted to obtain all nilpotent Lie superalgebras when $s(L) \leq 2$. Further, we apply those results to list all non-abelian nilpotent Lie superalgebras $L$ with $ t(L) \leq 4$.

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Saudamini Nayak. 2018-10-22. Classification of finite dimensional nilpotent Lie superalgebras by their multiplier. https://arxiv.org/abs/1810.09129

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