Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T14:46:50.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximal subsemigroups of Lie groups that are total

Published online by Cambridge University Press:  20 January 2009

Jimmie D. Lawson
Jimmie D. Lawson
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

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.

The major problem with which this paper is concerned is determining criteria that allow one to decide whether the subsemigroup generated by a subset B of a group G is all of G. Motivations for considering this problem arise from at least two sources.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 3 , October 1987 , pp. 479 - 501
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

REFERENCES

1.Bonnard, B., Jurdjevic, V., Kupka, I. and Sallet, G., Transitivity of families of invariant vector fields on the semidirect product of Lie groups, Trans. Amer. Math. Soc. 2 271 (1982), 525–535.CrossRefGoogle Scholar
2.Bourbaki, N., Topologie generale (Hermann, Paris, 1958).Google Scholar
3.Bourbaki, N., Lie Groups and Lie Algebras, I (Addison-Wesley, Reading, 1975).Google Scholar
4.Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, I (Amer. Math. Soc, 1961).CrossRefGoogle Scholar
5.Dobbins, J. G., Well-bounded semigroups in locally compact groups, Math. Z. 148 (1976), 155–167.CrossRefGoogle Scholar
6.Fuchs, L., Partially Ordered Algebraic Systems (Pergamon Press, 1963).Google Scholar
7.Gauthier, J., Kupka, I. and Sallet, G., Controllability of right invariant systems on real simple Lie groups (Preprint Institut Fourier, 1984).CrossRefGoogle Scholar
8.Hilgert, J., Maximal semigroups and controllability in products of Lie groups (Preprint THD Nr. 971, 1986).Google Scholar
9.Hilgert, J. and Hofmann, K., Old and new on SL(2), Manuscripta Math. 54 (1985), 17–52.CrossRefGoogle Scholar
10.Hilgert, J. and Hofmann, K., On Sophus Lie's Fundamental Theorems, J. Fund. Anal., to appear.Google Scholar
11.Hilgert, J., Hofmann, K. and Lawson, J. D., Controllability of systems on a nilpotent Lie group, Beiträge Algebra Geom. 30 (1985), 185–190.Google Scholar
12.Hilgert, J., Hofmann, K. and Lawson, J. D., The Lie Theory of Semigroups (Monograph, in preparation).CrossRefGoogle Scholar
13.Hofmann, K., Lie algebras with subalgebras of codimension one, Illinois J. Math. 9 (1965), 636–643.CrossRefGoogle Scholar
14.Hofmann, K. and Lawson, J., Foundations of Lie Semigroups (Lecture Notes in Math. 998, 1983), 128–201.Google Scholar
15.Hofmann, K. and Lawson, J., On Sophus Lie's Fundamental Theorems, I, Indag. Math. 45 (1983), 453–466.CrossRefGoogle Scholar
16.Hofmann, K. and Lawson, J. D., On Sophus Lie's Fundamental Theorems II, Indag. Math. 46 (1984), 255–265.CrossRefGoogle Scholar
17.Hochschild, G., The Structure of Lie Groups (Holden Day, San Francisco, 1965).Google Scholar
18.Jacobson, N., Lie Algebras (Dover, New York, 1962).Google Scholar
19.Jurdevic, V. and Kupka, I., Control systems on semisimple Lie groups and their homogeneous spaces, Ann. Inst. Fourier 31 (1981), 151–179.CrossRefGoogle Scholar
20.Ol'shanskii, G., Convex cones in symmetric Lie algebras, Lie semigroups, and invariant causal (order) structures on pseudo-Riemannian symmetric spaces, Soviet Math. Dokl. 26 (1982), 97–101.Google Scholar
21.Ol'shanskii, G., Invariant cones in symmetric Lie algebras, Lie semigroups, and the holomorphic discrete series, Functional Anal. Appl. 15 (1981), 275–285.CrossRefGoogle Scholar
22.Paneitz, S., Invariant convex cones and causality in semisimple Lie algebras and groups. J. Fund. Anal. 43 (1981), 313–359.CrossRefGoogle Scholar
23.Paneitz, S., Classification of invariant convex cones in simple Lie algebras, Ark. Mat. 21 (1984), 217–228.CrossRefGoogle Scholar
24.Poguntke, D., Well-bounded semigroups in connected groups, Semigroup Forum 15 (1977), 159–167.CrossRefGoogle Scholar
25.Sussman, H. and Jurdevic, V., Controllability of nonlinear systems, J. Differential Equations 12(1972), 95–116.CrossRefGoogle Scholar
26.Trrs, J., Sur une classe de groupes de Lie resolables, Bull Soc. Math. Belg. 11 (1959), 100–115.Google Scholar
27.Vinberg, E., Invariant cones and orderings in Lie groups, Functional Anal. Appl. 14 (1980), 1–13.CrossRefGoogle Scholar
28.Wright, F., Semigroups in compact groups, Proc. Amer. Math. Soc. 7 (1956), 309–311.CrossRefGoogle Scholar
29.Wright, F., Topological abelian groups, Amer. J. Math. 79 (1957), 477–496.CrossRefGoogle Scholar
30.Wright, F., Holder groups, Duke Math. J. 24 (1957), 567–571.CrossRefGoogle Scholar