On subsemigroups of semisimple Lie groups
El Assoudi, R. ; Gauthier, J. P. ; Kupka, I. A. K.
Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996), p. 117-133 / Harvested from Numdam
Publié le : 1996-01-01
@article{AIHPC_1996__13_1_117_0,
     author = {El Assoudi, R. and Gauthier, J. P. and Kupka, I. A. K.},
     title = {On subsemigroups of semisimple Lie groups},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {13},
     year = {1996},
     pages = {117-133},
     mrnumber = {1373474},
     zbl = {0848.93006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1996__13_1_117_0}
}
El Assoudi, R.; Gauthier, J. P.; Kupka, I. A. K. On subsemigroups of semisimple Lie groups. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) pp. 117-133. http://gdmltest.u-ga.fr/item/AIHPC_1996__13_1_117_0/

[1] B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Transitivity of families of invariant vector fields on the semi-direct products of Lie groups, Trans. Amer. Math. Soc., 1981. | Zbl 0519.49023

[2] N. Bourbaki, Groupes et algèbres de Lie, Fasc. XXXVIII, chap. 7-8, Hermann, Paris, 1975. | MR 453824

[3] R. El Assoudi,Accessibilité par des champs de vecteurs invariants à droite sur un groupe de Lie, Thèse de doctorat de l'Université Joseph Fourier, Grenoble, 1991.

[4] R. El Assoudi and J.P. Gauthier, Controllability of right invariant systems on real simple Lie groups of type F4, G2, Bn and Cn, Math. on Control signals systems, Vol. 1, 1988, pp. 293-301. | MR 961799 | Zbl 0672.93009

[5] J.P. Gauthier and G. Bornard, Controllabilité des systèmes bilinéaires, SIAM Journal on Control and Optimization, Vol. 20, (3), 1982, pp. 377-384. | MR 652214 | Zbl 0579.93005

[6] J.P. Gauthier, I. Kupka and G. Sallet, Controllability of right invariant systems on real simple Lie groups, Systems and control Letters, Vol. 5, 1984, pp. 187-190. | MR 777851 | Zbl 0552.93010

[7] S. Helgason, Differential geometry and symmetric spaces, Academic press, New York, 1962. | MR 145455 | Zbl 0111.18101

[8] J. Hilgert, Max. semigroups and controllability in products of Lie Groups, Archiv der Math., Vol. 49, 1987, pp. 189-195. | MR 906732 | Zbl 0649.22003

[9] J. Hilgert, K. Hoffman and J.D. Lawson, Controllability of systems on a nilpotent Lie Group, Beiträge Alg. Geom., Vol. 30, 1985, pp. 185-190. | MR 803388 | Zbl 0579.22010

[10] J. Hilgert, K. Hoffman and J.D. Lawson, Lie theory of semigroups, Technische Hochschule Darmstadt, Preprint, 1987.

[11] A. Joseph, The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. Sc. de l'École Normale Sup., 4e série, Vol. 9 (1), 1976, pp. 1-29. | Numdam | MR 404366 | Zbl 0346.17008

[12] V. Jurdjevic and I. Kupka, Controllability of right invariant systems on semi-simple Lie-Groups and their homogeneous spaces, Ann. Inst. Fourier, Grenoble, Vol. 31 (4), 1981, pp. 151-179. | Numdam | Zbl 0453.93011

[13] M. Kuranishi, On everywhere dense imbedding of free groups in Lie groups, Nagoya Math. Journal, Vol. 2, 1951, pp. 63-71. | MR 41145 | Zbl 0045.31003

[14] J.D. Lawson, Maximal subsemigroups of Lie Groups that are total, Proc. of Edimborough Math. Soc., Vol. 30, 1987, pp. 479-501. | MR 908455 | Zbl 0649.22004

[15] F.S. Leite, P.E. Crouch, Controllability on classical Lie Groups, Math. on Control, signals, systems, Vol. 1, 1988, pp. 31-42. | MR 923274 | Zbl 0658.93013

[16] G. Warner, Harmonic analysis on semi-simple Lie groups 1, Springer-Verlag, Berlin, 1972. | Zbl 0265.22020