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A new characterization of semisimple Lie algebras


Author: Said Benayadi
Journal: Proc. Amer. Math. Soc. 125 (1997), 685-688
MSC (1991): Primary 17B05, 17B20
DOI: https://doi.org/10.1090/S0002-9939-97-03612-5
MathSciNet review: 1353376
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Abstract: Using Casimir elements, we characterize the semisimple Lie algebras among the quadratic Lie algebras. This characterization gives, in particular, a generalization of a consequence of Cartan’s second criterion.


References [Enhancements On Off] (What's this?)

  • Saïd Benayadi, Une propriété nécessaire et suffisante pour qu’une algèbre de Lie sympathique quadratique soit semi-simple, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 11, 1155–1158 (French, with English and French summaries). MR 1309092
  • Saïd Benayadi, Structures de certaines algèbres de Lie quadratiques, Comm. Algebra 23 (1995), no. 10, 3867–3887 (French). MR 1348269, DOI https://doi.org/10.1080/00927879508825437
  • N. Bourbaki, Éléments de mathématique. Fasc. XXVI. Groupes et algèbres de Lie. Chapitre I: Algèbres de Lie, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1285, Hermann, Paris, 1971 (French). Seconde édition. MR 0271276

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Additional Information

Said Benayadi
Affiliation: Universite de Metz, Département de Mathematiques, U.R.A. CNRS n$^{\circ }$ 399, Ile du Saulcy, F-57045 Metz cedex 01, France
Email: benayadi@poncelet.univ-metz.fr

Keywords: Semisimple Lie algebras, quadratic Lie algebras, Casimir elements
Received by editor(s): May 4, 1995
Received by editor(s) in revised form: September 21, 1995
Communicated by: Roe Goodman
Article copyright: © Copyright 1997 American Mathematical Society