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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A quick proof of the classification
of simple real Lie algebras


Author: A. W. Knapp
Journal: Proc. Amer. Math. Soc. 124 (1996), 3257-3259
MSC (1991): Primary 17B20, 22E15
MathSciNet review: 1340392
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Abstract | References | Similar Articles | Additional Information

Abstract: Élie Cartan's classification of the simple Lie algebras over $\mathbb {R}$ is derived quickly from some structure theory over $\mathbb {R}$ and the classification over $\mathbb {C}$.


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

  • 1. N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968 (French). MR 0240238 (39 #1590)
  • 2. A. Borel and J. De Siebenthal, Les sous-groupes fermés de rang maximum des groupes de Lie clos, Comment. Math. Helv. 23 (1949), 200–221 (French). MR 0032659 (11,326d)
  • 3. Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978. MR 514561 (80k:53081)

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Additional Information

A. W. Knapp
Affiliation: Department of Mathematics, State University of New York, Stony Brook, New York 11794
Email: aknapp@ccmail.sunysb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03448-X
PII: S 0002-9939(96)03448-X
Received by editor(s): April 12, 1995
Communicated by: Roe W. Goodman
Article copyright: © Copyright 1996 American Mathematical Society