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Reduction de produits semi-directs et conjecture de Gel’fand et Kirillov. (French) Zbl 0415.17007


MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B35 Universal enveloping (super)algebras
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References:

[1] DIXMIER (J.) . - Sur les algèbres de Weyl , Bull. Soc. math. Fr., t. 96, 1968 , p. 209-242. Numdam | MR 39 #4224 | Zbl 0165.04901 · Zbl 0165.04901
[2] DIXMIER (J.) . - Algèbres enveloppantes . - Paris, Gauthier-Villars, 1974 (Cahiers scientifiques, 37). MR 58 #16803a | Zbl 0308.17007 · Zbl 0308.17007
[3] GEL’FAND (I. M.) et KIRILLOV (A. A.) . - Sur les corps liés aux algèbres enveloppantes des algèbres de Lie . - Paris, Presses universitaires de France, 1966 (Institut des hautes Études scientifiques, Publications mathématiques, 31, p. 5-20). Numdam | MR 34 #7731 | Zbl 0144.02104 · Zbl 0144.02104 · doi:10.1007/BF02684800
[4] GUICHARDET (A.) . - Communication privée .
[5] HERZ (J.) . - Pseudo-algèbres de Lie , C. R. Acad. Sc. Paris, t. 236, 1953 , série A, p. 1935-1937. MR 14,1057c | Zbl 0050.03201 · Zbl 0050.03201
[6] MACKEY (G. W.) . - Induced representations of locally compact groups , Annals of Math., t. 55, 1952 , p. 101-139 ; t. 58, 1953 , p. 193-221. MR 13,434a | Zbl 0051.01901 · Zbl 0051.01901 · doi:10.2307/1969786
[7] MARTINEZ ALONSO (L.) . - Group theoretical foundations of classical and quantum mechanics , I : Observables associated with Lie algebras, J. math. Phys., t. 18, 1977 , p. 1577-1581. MR 58 #32510 | Zbl 0373.22012 · Zbl 0373.22012 · doi:10.1063/1.523465
[8] MARTINEZ ALONSO (L.) . - Tesis doctoral , Dep. Fis. teor., Univ. Complut. Madrid, 1975 .
[9] NGHIEM-XUAN HAI . - Sous algèbres commutatives et représentations de l’algèbre enveloppante d’une algèbre de Lie résoluble , Thèse Sc. math. Univ. Pierre-et-Marie-Curie (Paris-VI), Paris, 1976 .
[10] NGHIEM-XUAN HAI . - Sur certaines représentations d’une algèbre de Lie résoluble complexe , II, Publ. Départ. Math. Orsay, n^\circ 213, 76-63. · Zbl 0275.17003
[11] RINEHART (G. S.) . - Differential form on general commutative algebras , Trans. Amer. math. Soc., t. 108, 1963 , p. 195-222. MR 27 #4850 | Zbl 0113.26204 · Zbl 0113.26204 · doi:10.2307/1993603
[12] RICHTI (R.) . - Twisted Hopf algebras . - Zürich, Forschungsinstitut für Mathematik, E.T.H., 1977 (Preprint).
[13] SCHWEBER (S.S.) . - An introduction to relativistic quantum field theory . - New York, Harper and Row, 1961 (Harper international Student Reprint). MR 23 #B841 | Zbl 0111.43102 · Zbl 0111.43102
[14] WARNER (G.) . - Harmonic analysis on semi simple Lie groups , Vol. I and II. - Berlin, Springer-Verlag, 1972 (Grundlehren der mathematischen Wissenschaften, 188-189). Zbl 0265.22020 · Zbl 0265.22020
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