Split Malcev algebras |
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Authors: | ANTONIO J CALDERóN MARTíN MANUEL FORERO PIULESTáN JOSé M SáNCHEZ DELGADO |
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Institution: | 1. Departamento de Matem??ticas, Universidad de C??diz, 11510, Puerto Real, C??diz, Spain
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Abstract: | We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras M is of the form $M={\mathcal U} +\sum_{j}I_{j}$ with ${\mathcal U}$ a subspace of the abelian Malcev subalgebra H and any I j a well described ideal of M satisfying I j ,I k ]?=?0 if j????k. Under certain conditions, the simplicity of M is characterized and it is shown that M is the direct sum of a semisimple split Lie algebra and a direct sum of simple non-Lie Malcev algebras. |
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