Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-22T20:20:03.251Z Has data issue: false hasContentIssue false
  • English
  • Français

Representations of Lie Groups by Contact Transformations, II: Non-Compact Simple Groups

Published online by Cambridge University Press:  20 November 2018

Carl Herz
Carl Herz*
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montreal, Quebec, H3A 2K6
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If a Lie group acts faithfully as a transitive group of contact transformations of a compact manifold it is either compact with centre of dimension at most 1 or non-compact simple. The latter case is described

Résumé

Résumé

Si un groupe de Lie se présente comme groupe transitif de transformations de contact de variété compacte, alors il est ou compact de centre de dimension au plus un ou non-compact simple de centre fini. On décrit ce qui se passe dans le second cas.

Keywords

22E4622E15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 778 - 802
Copyright
Copyright © Canadian Mathematical Society 1993

References

Cartan, E. (1893), Sur la structure des groupes simples finis et continus C. R. Acad. Sci. Paris 116, 784–786.Google Scholar
Engel, F. (1893), Sur un groupe simple quatorze paramètres, C. R. Acad. Sci. Paris 116, 786–788.Google Scholar
Freudenthal, H. and deVries, H. (1969), Linear Lie Groups, Academic Press, New York and London.Google Scholar
Herz, C. (1991), Representations of Lie groups by contact transformations, I: Compact Groups, Canad. Math. Bull. 33, 369–375.Google Scholar
Steenrod, N. (1951), The Topology of Fibre Bundles, Princeton University Press, Princeton.Google Scholar
Warner, G. (1972), Harmonie Analysis on Semi-Simple Lie Groups I, Springer-Verlag, New York-Heidelberg- Berlin.Google Scholar
Wolf, J. A. (1978), Representations associated to minimal co-adjoint orbits, Differential and Geometric methods in mathematical physics, II, 329-349, Lecture Notes in Math. 676, Springer, Berlin.Google Scholar