Hostname: page-component-6bb9c88b65-2jdt9 Total loading time: 0 Render date: 2025-07-24T16:21:33.911Z Has data issue: false hasContentIssue false
  • English
  • Français

Exponentiality of Certain Real Solvable Lie Groups

Published online by Cambridge University Press:  20 November 2018

Martin Moskowitz  and
Michael Wüstner
Martin Moskowitz
Affiliation:
Department of Mathematics CUNY Graduate Center 33 W 42 Street New York NY 10036 USA, e-mail: mmoskowi@email.gc.cuny.edu
Michael Wüstner
Affiliation:
Fachbereich Mathematik Technische Universität Darmstadt Schloßgartenstraße 7 64289 Darmstadt Germany, e-mail: wuestner@mathematik.tu-darmstadt.de
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.

In this article, making use of the second author’s criterion for exponentiality of a connected solvable Lie group, we give a rather simple necessary and sufficient condition for the semidirect product of a torus acting on certain connected solvable Lie groups to be exponential.

Keywords

22E2522E15

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 368 - 373
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Bourbaki, N., Éléments de Mathématique, Groupes et Alge`bres de Lie, Chap. I. Hermann, Paris, 1971.Google Scholar
2. Bourbaki, N., Éléments de Mathématique, Groupes et Alge`bres de Lie, Chap. VII. Hermann, Paris, 1975.Google Scholar
3. Chevalley, C., Théorie des Groupes de Lie III. Hermann, Paris, 1955.Google Scholar
4. Dixmier, J., L’application exponentielle dans les groupes de Lie résolubles. Bull. Math. Soc. France 85 (1957), 113–121.Google Scholar
5. Djokovic, D. and Nguyen, T., On the exponential map of almost simple real algebraic groups. J. Lie Theory 5 (1996), 275–291.Google Scholar
6. Hofmann, K. H., A memo on the exponential function and regular points. Arch.Math. 59 (1992), 24–37.Google Scholar
7. Hofmann, K. H. and Lawson, J. D., Divisible subsemigroups of Lie groups. J. LondonMath. Soc. 27 (1983), 427–437.Google Scholar
8. Hofmann, K. H. and Mukherjea, A., On the density of the image of the exponential function. Math. Ann. 234 (1978), 263–273.Google Scholar
9. Moskowitz, M., On the surjectivity of the exponential map in certain Lie groups. Ann. Mat. Pura Appl. Ser. 4 166 (1994), 129–143.Google Scholar
10. Moskowitz, M., Correction and addenda to: On the surjectivity of the exponential map in certain Lie groups. Ann. Mat. Pura Appl. (to appear).Google Scholar
11. Neeb, K.-H., Weakly Exponential Lie Groups. J. Alg. 179 (1996), 331–361.Google Scholar
12. Saito, M., Sur certaines groupes de Lie resolubles. Sci. Pap. Coll. Gen. Ed. Univ. Tokyo, 7 (1957), 1–11.Google Scholar
13. Wüstner, M., On the surjectivity of the exponential function of solvable Lie groups. Math. Nachr. (1998) (to appear).Google Scholar