Leibniz Algebras Whose Semisimple Part is Related to sl2
In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras sl1 2⊕sl2 2⊕· · ·⊕sls 2⊕R, where R is a solvable radical. The classifications of such Leibniz algebras in the cases dimR = 2, 3 and dimI 6= 3 have been obtained. Moreover, we classify...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/90253 |
| Acesso em linha: | https://hdl.handle.net/11441/90253 https://doi.org/10.1007/s40840-017-0458-z |
| Access Level: | acceso abierto |
| Palavra-chave: | Leibniz algebra Simple algebra sl2, Direct sum of algebras Right module Irreducible module |
| Resumo: | In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras sl1 2⊕sl2 2⊕· · ·⊕sls 2⊕R, where R is a solvable radical. The classifications of such Leibniz algebras in the cases dimR = 2, 3 and dimI 6= 3 have been obtained. Moreover, we classify Leibniz algebras with L/I ∼= sl1 2⊕sl2 2 and some conditions on ideal I = id < [x, x] | x ∈ L > |
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