Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-20T15:19:37.822Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Relationship Between Adjoint Orbits and Conjugacy Classes of a Lie Group

Published online by Cambridge University Press:  20 November 2018

N. J. Wildberger
N. J. Wildberger*
Affiliation:
University of New South Wales Kensington, NSW 2033 Australia
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.

Let G be a Lie group with adjoint orbits θi and corresponding conjugacy classes Ci = exp θi, i = 1, 2, 3. We show that if G is nilpotent or compact, there is a neighbourhood U of 0 in g such that if θi ∊ U then θ3 ⊂ θ1 + θ2 if and only if C3 ⊂ C1C2.

Keywords

22E15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 297 - 304
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Jacobson, N., Lie Algebras, John Wiley and Sons (1962), New York.Google Scholar
2. Kirillov, A. A., The characters of unitary representations of Lie groups, Funct. Anal, and its Applications 2, No. 2 (1968), 133–146.Google Scholar
3. Thompson, R., Author vs Referee: A Case History for Middle Level Mathematicians, Amer. Math. Monthly 90, No. 10 (1983), 661–668.Google Scholar
4. Weil, A., Lintegration dans les groups topologiques et ses application., Actualités Sci. et Ind. 869, 1145 (1941), Hermann and Cie, Paris.Google Scholar
5. Weyl, H., Gruppen théorie und Quantenmechanik 2. Aufl., S. Hirzel (1931), Leipzig.Google Scholar