Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



A new characterization
of semisimple Lie algebras

Author: Said Benayadi
Journal: Proc. Amer. Math. Soc. 125 (1997), 685-688
MSC (1991): Primary 17B05, 17B20
MathSciNet review: 1353376
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 17B05, 17B20

Retrieve articles in all journals with MSC (1991): 17B05, 17B20

Additional Information

Said Benayadi
Affiliation: Universite de Metz, Département de Mathematiques, U.R.A. CNRS n$^{∘}$ 399, Ile du Saulcy, F-57045 Metz cedex 01, France

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

American Mathematical Society