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arXiv · 1905.00845

On Leibniz superalgebras which even part is sl_2

Kh. A. Khalkulova·A. Kh. Khudoyberdiyev
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Abstract

This article deals with a Leibniz superalgebras $L=L_0\oplus L_1,$ whose even part is a simple Lie algebra $\mathfrak{sl}_2$. We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on $\mathfrak{sl}_2 $. We show that there exist such Leibniz superalgebras with nontrivial odd part only in case of $dim L_1=2.$

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Kh. A. Khalkulova, A. Kh. Khudoyberdiyev. 2019-05-02. On Leibniz superalgebras which even part is sl_2. https://arxiv.org/abs/1905.00845

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