Simple left-symmetric algebras with solvable Lie algebra |
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Authors: | Dietrich Burde |
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Affiliation: | 1. Mathematisches Institut der Universit?t Düsseldorf, D-40225, Düsseldorf, Germany
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Abstract: | Left-symmetric algebras (LSAs) are Lie admissible algebras arising from geometry. The leftinvariant affine structures on a Lie groupG correspond bijectively to LSA-structures on its Lie algebra. Moreover if a Lie group acts simply transitively as affine transformations on a vector space, then its Lie algebra admits a complete LSA-structure. In this paper we studysimple LSAs having only trivial two-sided ideals. Some natural examples and deformations are presented. We classify simple LSAs in low dimensions and prove results about the Lie algebra of simple LSAs using a canonical root space decomposition. A special class of complete LSAs is studied. |
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