An Artinian theory for Lie algebras |
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Authors: | Antonio Fernández López Esther García Miguel Gómez Lozano |
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Affiliation: | 1. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Málaga, Spain;2. Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain |
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Abstract: | Complemented Lie algebras are introduced in this paper (a notion similar to that studied by O. Loos and E. Neher in Jordan pairs). We prove that a Lie algebra is complemented if and only if it is a direct sum of simple nondegenerate Artinian Lie algebras. Moreover, we classify simple nondegenerate Artinian Lie algebras over a field of characteristic 0 or greater than 7, and describe the Lie inner ideal structure of simple Lie algebras arising from simple associative algebras with nonzero socle. |
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