Split Malcev algebras
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- 作者：ANTONIO J CALDERóN MARTíN (1) ajesus.calderon@uca.es
MANUEL FORERO PIULESTáN (1) ForeroManuel@hotmail.com
JOSé M SáNCHEZ DELGADO (1) josemaria.sanchezdelgado@alum.uca.es - 关键词：Malcev algebras – structure theory – roots – root spaces
- 刊名：Proceedings Mathematical Sciences
- 出版年：2012
- 出版时间：May 2012
- 年：2012
- 卷：122
- 期：2
- 页码：181-187
- 全文大小：203.5 KB
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- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer India
- ISSN：0973-7685
文摘
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=U +?jIjM={\mathcal U} +\sum_{j}I_{j} with U{\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.