Some remarks on Leibniz algebras whose semisimple part related with $sl_2$
L.M. CamachoMatemática Aplicada I . Universidad de Sevilla. Avda. Reina Mercedes , s/n . 41012 Sevilla . ( SpainS. G ́ Omez-VidalKarimjanov ] Institute of Mathematics and Information Technologies of Academy of Uzbekistan , 29, Do'rmon yo'li street. , 100125 , Tashkent ( Uzbekistan)B. A. OmirovMatemática Aplicada I . Universidad de Sevilla. Avda. Reina Mercedes , s/n . 41012 Sevilla . ( SpainI. A. KarimjanovMatemática Aplicada I . Universidad de Sevilla. Avda. Reina Mercedes , s/n . 41012 Sevilla . ( Spain
2013en
ABI
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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 $I=id.$
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