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

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

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

Rings and Algebras 2014-09-15 v2 Representation Theory

Authors: L. M. Camacho , S. Gómez-Vidal , B. A. Omirov , I. A. Karimjanov

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 $I=id<[x,x] \ | \ x\in L>.$

Keywords

Leibniz algebras Lie algebras semisimple part $sl_2$ solvable radical classification finite-dimensional

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@article{arxiv.1310.6594,
  title  = {Some remarks on Leibniz algebras whose semisimple part related with $sl_2$},
  author = {L. M. Camacho and S. Gómez-Vidal and B. A. Omirov and I. A. Karimjanov},
  journal= {arXiv preprint arXiv:1310.6594},
  year   = {2014}
}

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11 pages

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

Abstract

Keywords

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