Some remarks on Leibniz algebras whose semisimple part related with $s{l}_2$

Abstract

In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $s{l}_2^1\oplus s{l}_2^2\oplus \cdots \oplus s{l}_2^s\oplus R,$ where $R$ is a solvable radical. The classifications of such Leibniz algebras in the cases $dimR=2,3$ and $dimI\ne 3$ have been obtained. Moreover, we classify Leibniz algebras with $L/I\cong s{l}_2^1\oplus s{l}_2^2$ and some conditions on ideal $I=id<[x,x]|x\in L>.$

11 pages

References in corpus (1)

• Leibniz algebras with associated Lie algebras sl_2\dot{+} R (dim R=2)