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arXiv · 1310.6594

Some remarks on Leibniz algebras whose semisimple part related with $sl_2$

L. M. Camacho·S. Gómez-Vidal·B. A. Omirov·I. A. Karimjanov
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Abstract

In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $sl_2^1\oplus sl_2^2\oplus \dots \oplus sl_2^s\oplus R,$ where $R$ is a solvable radical. The classifications of such Leibniz algebras in the cases $dim R=2, 3$ and $dim I\neq 3$ have been obtained. Moreover, we classify Leibniz algebras with $L/I\cong sl_2^1\oplus sl_2^2$ and some conditions on ideal $I=id<[x,x] \ | \ x\in L>.$

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L. M. Camacho, S. Gómez-Vidal, B. A. Omirov, I. A. Karimjanov. 2014-09-11. Some remarks on Leibniz algebras whose semisimple part related with $sl_2$. https://arxiv.org/abs/1310.6594

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