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)

 
 

 

Generating sets
for compact semisimple Lie groups


Author: Michael Field
Journal: Proc. Amer. Math. Soc. 127 (1999), 3361-3365
MSC (1991): Primary 22E15
DOI: https://doi.org/10.1090/S0002-9939-99-04959-X
Published electronically: May 4, 1999
MathSciNet review: 1618662
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $\Gamma$ be a compact connected semisimple Lie group. We prove that the subset of $\Gamma^2$ consisting of pairs $(g, h)$ which topologically generate $\Gamma$ is Zariski open.


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

  • 1. J F Adams. Lectures on Lie Groups. The University of Chicago Press, Chicago and London, 1982.
  • 2. H Auerbach. `Sur les groupes linéaires bornés (III)', Studia Mat, V (1934), 43-49.
  • 3. T Bröcker and T tom Dieck. Representations of Compact Lie Groups, Springer-Verlag, New York, 1985. MR 86i:22023
  • 4. C W Curtis and I Reiner. Representation Theory of Finite Groups and Associative Algebras, (Interscience Publishers, John Wiley and sons, New York-London, 1962). MR 26:2519
  • 5. M J Field and W Parry. `Stable ergodicity of skew extensions by compact Lie groups', Topology 38 (1999), 167-187. CMP 98:17
  • 6. M Goto. `A theorem on compact semi-simple groups', J. Math. Soc. Japan 1 (1949), 270-272. MR 11:497d
  • 7. K H Hofmann and S A Morris, `Weight and c', J. of Pure and Applied Algebra 68 (1990), 181-194. MR 92g:22011
  • 8. M Kuranishi. `Two element generations on semi-simple Lie groups', Kodai math. Sem. Report, (1949), 9-10. MR 11:640a
  • 9. M Kuranishi. `On everywhere dense imbedding of free groups in Lie groups', Nagoya Math. J. 2 (1951), 63-71. MR 12:802c
  • 10. A L Onishchik and E B Vinberg. Lie Groups and Algebraic Groups, Springer-Verlag, Berlin, Heidelberg, New York, 1990. MR 91g:22001
  • 11. J Schreier et S Ulam, `Sur le nombre des générateurs d'un groupe topologique compact et connexe', Fund. Math. 24 (1935), 302-304.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 22E15

Retrieve articles in all journals with MSC (1991): 22E15


Additional Information

Michael Field
Email: mf@uh.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04959-X
Received by editor(s): September 24, 1997
Received by editor(s) in revised form: January 20, 1998
Published electronically: May 4, 1999
Additional Notes: This research was supported in part by NSF Grant DMS-1551704 and Texas Advanced Research Program Award 1127681
Communicated by: Roe W. Goodman
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society