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A new characterization of semisimple Lie algebras

Author(s): Said Benayadi
Journal: Proc. Amer. Math. Soc. 125 (1997), 685-688.
MSC (1991): Primary 17B05, 17B20
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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:

[B1]: S. Benayadi, Une propriété nécessaire et suffisante pour qu'une algèbre de, C.R. Acad. Sci. Paris, t. 319 (1994), 1155-1158. MR 95m:17009
[B2]: -, Structures de certaines algèbres de Lie quadratiques, Comm. in Algebra (to appear). MR 96h:17004
[Bo]: N. Bourbaki, Groupes et algèbres de Lie, Hermann, Paris, 1971. MR 42:6159

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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

DOI: 10.1090/S0002-9939-97-03612-5
PII: S 0002-9939(97)03612-5
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
Copyright of article: Copyright 1997, American Mathematical Society


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