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arXiv · 1411.6508

Leibniz algebras associated with representations of filiform Lie algebras

Sh. A. Ayupov·L. M. Camacho·A. Kh. Khudoyberdiyev·B. A. Omirov
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Abstract

In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra $n_{n,1}.$ We introduce a Fock module for the algebra $n_{n,1}$ and provide classification of Leibniz algebras $L$ whose corresponding Lie algebra $L/I$ is the algebra $n_{n,1}$ with condition that the ideal $I$ is a Fock $n_{n,1}$-module, where $I$ is the ideal generated by squares of elements from $L$.

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Sh. A. Ayupov, L. M. Camacho, A. Kh. Khudoyberdiyev, B. A. Omirov. 2014-11-24. Leibniz algebras associated with representations of filiform Lie algebras. https://doi.org/10.1016/j.geomphys.2015.08.002

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