On Real Simple Left-symmetric Algebras |
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Authors: | Xiaoli Kong Daoji Meng |
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Institution: | 1. Department of Mathematical Sciences , University of Kentucky , Lexington , Kentucky , USA;2. Department of Mathematics and LPMC , Nankai University , Tianjin , China |
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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. |
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Keywords: | Real form Real left-symmetric algebra Semi-involution Simple left-symmetric algebra |
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