Article
Leibniz algebras with associated Lie algebras sl_2\dot{+} R (dim R=2)
Author/s | Camacho Santana, Luisa María
Gómez Vidal, S. Omirov, Bakhrom Abdazovich |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2011 |
Deposit Date | 2019-11-11 |
Published in |
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Abstract | From the theory of finite dimensional Lie algebras it is known that
every finite dimensional Lie algebra is decomposed into a semidirect sum of
semisimple subalgebra and solvable radical. Moreover, due to work of ... From the theory of finite dimensional Lie algebras it is known that every finite dimensional Lie algebra is decomposed into a semidirect sum of semisimple subalgebra and solvable radical. Moreover, due to work of Mal’cev the study of solvable Lie algebras is reduced to the study of nilpotent ones. For the finite dimensional Leibniz algebras the analogues of the mentioned results are not proved yet. In order to get some idea how to establish the results we examine the Leibniz algebra for which the quotient algebra with respect to the ideal generated by squares elements of the algebra (denoted by I) is a semidirect sum of semisimple Lie algebra and the maximal solvable ideal. In this paper the class of complex Leibniz algebras, for which quotient algebras by the ideal I are isomorphic to the semidirect sum of the algebra sl2 and two-dimensional solvable ideal R, are described. |
Citation | Camacho Santana, L.M., Gómez Vidal, S. y Omirov, B.A. (2011). Leibniz algebras with associated Lie algebras sl_2\dot{+} R (dim R=2). ArXiv.org, arXiv:1111.4631 |
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