Abstract:
Left-symmetric algebras (LSAs) are Lie admissible algebras arising from geometry. The leftinvariant affine structures on a Lie group {G} 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 study simple 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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Received: 10 June 1997 / Revised version: 29 September 1997
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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/s002290050037
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DOI: https://doi.org/10.1007/s002290050037