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Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie

Published online by Cambridge University Press:  20 November 2018

Thierry Robart
Thierry Robart*
Affiliation:
Department of Mathematics, McGill University, Montreal, Quebec, H3A 2K6 e-mail: [email protected]
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Abstract

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Keywords

Première: 22E6558h05Seconde: 17B65
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 820 - 839
Copyright
Copyright © Canadian Mathematical Society 1997

References

[BaD 93] Banyaga, A., Donato, P., Some remarks on the integration of the Poisson algebra, C.P.T Luminy Marseille, 1993. prépublication.Google Scholar
[Bas 64] Bastiani, A., Applications différentiables et variétés différentiables de dimension infinie. J. Analyse Math. 13(1964), 1–114.Google Scholar
[Bir 38] Birkhoff, G., Analytical groups. Tr.A.M.S. 43(1938), 61–101.Google Scholar
[Bou 72] Bourbaki, N., Groupes et algèbres de Lie, (Hermann, Paris) Chap. 2,3, 1972.Google Scholar
[BS b71] Bochnak, J., Siciak, J., Analytic functions in topological vector spaces, Studia Mathematica, t.XXXIX, 1971.Google Scholar
[Che 46] Chevalley, C., Theory of Lie Groups, I, Princeton University Press, Princeton, 1946.Google Scholar
[Daz 85] Dazord, P., Feuilletages à singularités. Nederl AkadWetensch Proc Ser.A-88 (1), IndagationesMath. 47(1985), 21–39.Google Scholar
[Daz 93] Dazord, P., Lie groups and algebras in infinite dimension: a new approach, XXXIII Taniguchi Symposium, Symplectic Geometry and its applications, 1993.Google Scholar
[Ebi 70] Ebin, D.G., Marsden, J.,Groups of diffeomorphisms and the motion of an incompressible fluid. Annals of Math. (1) 92(1970).Google Scholar
[Har 72] de la Harpe, P., Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space. Springer, 285, 1972.Google Scholar
[Köt 69] Köthe, G., Topological Vector Spaces I. Die Grund. der Math. Wiss. 159 Springer Verlag, 1969.Google Scholar
[Les 67] Leslie, J., On a differential structure for the group of diffeomorphisms. Topology 6(1967), 264–271.Google Scholar
[Les 87] Leslie, J., On the subgroups of infinite dimensional Lie groups. Bull. of A.M.S. (1) 16(1987).Google Scholar
[Les 92] Leslie, J., Some integrable subalgebras of the Lie algebras of infinite-dimensional Lie groups. Trans. of the A.M.S. 333(1992), 423–443.Google Scholar
[Les 93] Leslie, J., On the integrability of some infinite dimensional Lie Algebras, Howard University (Washington DC), preprint.Google Scholar
[Mil 82] Milnor, J., On infinite dimensional Lie groups, September, 1982.(unpublished).Google Scholar
[Mil 83] Milnor, J., Remarks on infinite dimensional Lie groups, Proceedings of Summer School on quantum Gravity, les Houches, session XL, North-Holland, 1983. p. 1007–1057.Google Scholar
[NRW94] Natarajan, L., Rodriguez-Carrington, E., Wolf, J.A., New classes of infinite-dimensional Lie groups. Proc Sympos Pure Math (2) 56(1994), 377–392.Google Scholar
[Olv 86] Olver, P.J., Applications of Lie groups to differential equations, Springer-Verlag, 107, 1986.Google Scholar
[Omo 74] Omori, H., Infinite dimensional Lie transformation groups. Lecture Notes in Math. 427, Springer- Verlag, 1974.Google Scholar
[Omo 73] Omori, H., Groups of diffeomorphisms and their subgroups. Trans. A.M.S. 178(1973).Google Scholar
[OMYK 81] Omori, H., Maeda, Y., Yoshioka, A., Kobayashi, O., On regular Fréchet-Lie groups. Tokyo J. Math. (2) 5(1981), 365–397.Google Scholar
[Rob 94] Robart, T., Thèse, Université Aix-Marseille II, 1994.Google Scholar
[Rob 96] Robart, T., Groupes de Lie de dimension infinie. Second et troisième théorèmes de Lie. I - Groupes de première espèce. C. R. Acad. Sci. Paris, t. 322, Série I, p. 1071–1074, 1996.Google Scholar
[RoK 97] Robart, T., Kamran, N., Sur la théorie locale des pseudogroupes de transformations continus infinis, Math. Annalen, 1997.(à paraître).Google Scholar
[Sou 85] Souriau, J-M., Un algorithme générateur de structures quantiques, Société Mathématique de France, Astérisque, hors série, 1985. p. 341–399.Google Scholar
[Stf 74] Stefan, P., Accessibility and foliations with singularities. Bull Am.Math. Soc. (6) 80(1974), 1142–1145.Google Scholar
[Sus 73] Sussmann, H.J., Orbits of families of vector fields and integrability of distributions. Trans Am. Math. Soc. 180(1973), 171–188.Google Scholar