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manuscripta mathematica

, Volume 95, Issue 3, pp 397–411 | Cite as

Simple left-symmetric algebras with¶solvable Lie algebra

  • Dietrich Burde

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.

Keywords

Vector Space Special Class Affine Transformation Space Decomposition Root Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Dietrich Burde
    • 1
  1. 1.Mathematisches Institut der Universität Düsseldorf, D-40225 Düsseldorf, GermanyDE

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