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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
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:
- [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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