1. On Real Simple Left-symmetric Algebras.
- Author
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Kong, Xiaoli, Bai, Chengming, and Meng, Daoji
- Subjects
- *
MATHEMATICAL symmetry , *MATHEMATICAL forms , *ALGEBRAIC geometry , *DIMENSION theory (Algebra) , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
In this article, we commence to study the real (simple) left-symmetric algebras. From the known classification of certain complex (semi)simple left-symmetric algebras, we classify their corresponding real forms. We not only obtain the classification of real simple left-symmetric algebras in low dimensions, but also find certain examples of real simple left-symmetric algebras in higher dimensions. In particular, there exists a complex simple left-symmetric algebra without any real form. We also give a geometric construction for a class of real simple left-symmetric algebras. At last, we apply the classification results to study some structures related to geometry. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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