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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A new characterization of semisimple Lie algebras
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by Said Benayadi PDF
Proc. Amer. Math. Soc. 125 (1997), 685-688 Request permission


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.
  • 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 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:
  • Received by editor(s): May 4, 1995
  • Received by editor(s) in revised form: September 21, 1995
  • Communicated by: Roe Goodman
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 685-688
  • MSC (1991): Primary 17B05, 17B20
  • DOI:
  • MathSciNet review: 1353376