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Simple left-symmetric algebras with solvable Lie algebra

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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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  1. Mathematisches Institut der Universität Düsseldorf, D-40225, Düsseldorf, Germany

    Dietrich Burde

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  1. Dietrich Burde
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Burde, D. Simple left-symmetric algebras with solvable Lie algebra. Manuscripta Math 95, 397–411 (1998). https://doi.org/10.1007/BF02678039

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  • DOI: https://doi.org/10.1007/BF02678039

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