Déformations de $C^{*}$-algèbres de Hopf

Blanchard, Etienne

Bulletin de la Société Mathématique de France, Tome 124 (1996) no. 1, pp. 141-215.

[1] Baaj (S.). - Thèse, Université Pierre et Marie Curie, Paris, 1980.

[2] Baaj (S.). - Représentation régulière du groupe quantique Eμ(2) de Woronowicz, C. R. Acad. Sci. Paris, t. 314, 1992, p. 1021-1026. | MR | Zbl

[3] Baaj (S.). - Représentation régulière du groupe quantique des déplacements de Woronowicz, preprint.

[4] Baaj (S.) et Skandalis (G.). - Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres, Ann. Sci. École Norm. Sup. (4), t. 26, 1993, p. 425-488. | EuDML | Numdam | MR | Zbl

[5] Bartle (R.G.) and Graves (L.M.). - Mappings between function spaces, Trans. Amer. Math. Soc., t. 72, 1952, p. 400-413. | MR | Zbl

[6] Bauval (A.). - Déformation du groupe de Lie-Poisson SU(2), prépublication n° 13 de l'URA 1408, Toulouse, 1992.

[7] Bauval (A.). - RKK(X)-nucléarité (d'après G. Skandalis), preprint.

[8] Blackadar (B.). - K-theory for Operator Algebras, Math. Sci. Res. Inst. Publ., t. 5, 1986. | MR | Zbl

[9] Blanchard (E.). - Représentations de champs de C*-algèbres, C.R. Acad. Sci. Paris, t. 314, 1992, p. 911-914. | MR | Zbl

[10] Bourbaki (N.). - Espace vectoriels topologiques. - Hermann et Cie, Paris, 1955.

[11] Choi (M.D.) and Effros (E.G.). - Nuclear C*-algebras and injectivity : the general case, Indiana Univ. Math. J., t. 26, 1977, p. 443-446. | MR | Zbl

[12] Cohen (P.J.). - Factorization in group algebras, Duke Math. J., t. 26, 1959, p. 199-205. | MR | Zbl

[13] Connes (A.). - Classification of injective factors, Ann. of Math., t. 104, 1976, p. 73-115. | MR | Zbl

[14] Dixmier (J.). - Les C*-algèbres et leurs représentations. - Gauthiers-Villars, Paris, 1969. | MR | Zbl

[15] Drinfel'D (V.G.). - Quantum groups. - Proceedings of the I.C.M., Berkeley, California, 1986.

[16] Dupré (M.J.). - The classification and structure of C*-algebra bundles, Mem. Amer. Math. Soc., t. 222, 1979. | MR | Zbl

[17] Effros (E.G.) and Lance (E.C.). - Tensor products of operator algebras, Adv. in Math., t. 25, 1977, p. 1-34. | MR | Zbl

[18] Elliott (G.), Natsume (T.) and Nest (R.). - The Heisenberg Group and K-Theorie, K-Theory, t. 7, 1993, p. 409-428. | MR | Zbl

[19] Enock (M.) et Schwartz (J.M.). - Une dualité dans les algèbres de von Neumann, Mémoire Soc. Math. France, suppl. Bull., n° 44, 1975, p. 1-144. | Numdam | MR | Zbl

[20] Enock (M.) et Schwartz (J.M.). - Algèbres de Kac moyennables, Pacific J. Math., t. 125, 2, 1986, p. 363-379. | MR | Zbl

[21] Fell (J.M.G.). - The structure of algebras of operator fields, Acta Math., t. 106, 1962, p. 237-268. | Zbl

[22] Gelfand (I.M.) and Nairmark (M.A.). - On the embedding of normed rings into the ring of operators in Hilbert space, Mat. Sb., t. 12, 1943, p. 197-213. | Zbl

[23] Green (P.). - The local structure of twisted covariance algebras, Acta Math., t. 140, 1978, p. 191-250. | MR | Zbl

[24] De La Harpe (P.) et Valette (A.). - La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque n° 175, 1989.

[25] Kac (G.I.). - Ring groups and the duality principle, Trans. Moscow Math. Soc., 1963, p. 291-339 (traduit de Trudy Moskov. Math. Obshch., t. 12, 1963, p. 259-301). | MR | Zbl

[26] Kasparov (G.G.). - Hilbert C*-modules : theorems of Stinespring aand Voiculescu, J. Operator Theory, t. 4, 1980, p. 133-150. | MR | Zbl

[27] Kasparov (G.G.). - Equivariant KK-theory and the Novikov conjecture, Invent. Math., t. 91, 1988, p. 147-201. | MR | Zbl

[28] Katayama (Y.). - Takesaki's duality for a non degenerate coaction, Math. Scand., t. 55, 1985, p. 141-151. | MR | Zbl

[29] Kirchberg (E.). - On non-semisplit extension, tensor products and exactness of group C*-algebras, Invent. Math., t. 112, 1993, p. 449-489. | MR | Zbl

[30] Kirchberg (E.) and Wassermann (S.). - Operations on continuous bundles of C*-algebras, preprint.

[31] Lance (C.). - Tensor product and nuclear C*-algebras, Operator Algebras and Applications, Proc. Sympos. Pure Math., t. 38, I, 1982, p. 379-399. | MR | Zbl

[32] Lee (R.-Y.). - On the C*-algebras of operator fields, Indiana Univ. Math. J., t. 25, 1976, p. 303-314. | MR | Zbl

[33] Masuda (T.), Mimachi (K.), Nakagami (Y.), Noumi (M.) and Ueno (K.). - Representations of quantum groups and a q-analogue of orthogonal polynomials, C. R. Acad. Sci. Paris, t. 307, 1988, p. 559-564. | MR | Zbl

[34] Michael (E.). - Continuous selection I, Ann. Math., t. 63, 1956, p. 361-382. | MR | Zbl

[35] Nagy (G.). - A framework for deformation quantization, thesis, Berkeley, 1992.

[36] Nagy (G.). - On the Haar measure of the quantum SU(N) group, Comm. Math. Phys., t. 153, 1993, p. 217-228. | MR | Zbl

[37] Paschke (W.). - Inner product modules over B*-algebras, Trans. Amer. Math. Soc., t. 182, 1973, p. 443-468. | MR | Zbl

[38] Pedersen (G.K.). - C*-algebras and their automorphism groups. - Academic press, 1979. | MR | Zbl

[39] Podles (P.) and Woronowicz (S.L.). - Quantum deformation of Lorentz group, Comm. Math. Phys., t. 130, 1990, p. 381-431. | MR | Zbl

[40] Rieffel (M.A.). - Continuous fields of C*-algebras coming from group cocycles and actions, Math. Ann., t. 283, 1989, p. 631-643. | MR | Zbl

[41] Rieffel (M.A.). - Deformation quantization of Heisenberg manifolds, Comm. Math. Phys., t. 122, 1989, p. 531-562. | MR | Zbl

[42] Sheu (J.L.). - Quantization of the Poisson SU(2) and its Poisson homogeneous space, the 2-sphere, Comm. Math. Phys., t. 135, 1991, p. 217-232. | MR | Zbl

[43] Skandalis (G.). - Operator algebras and duality, Proc. Intern. Congr. Math., t. 2, 1990, p. 997-1009. | MR | Zbl

[44] Stratila (S.). - Modular theory in operator algebras. - Academiei and Abacus Press, 1981. | MR | Zbl

[45] Takesaki (M.). - On the cross norm of the direct product of C*-algebras, Tôhoku Math. J., t. 16, 1964, p. 111-122. | MR | Zbl

[46] Tomiyama (J.). - Topological representation of C*-algebras, Tôhoku Math. J., t. 14, 1962, p. 187-204. | MR | Zbl

[47] Valin (J.M.). - C*-algèbres de Hopf et C*-algèbres de Kac, Proc. London Math. Soc. (3), t. 50, 1985, p. 131-174. | MR | Zbl

[48] Voiculescu (D.). - Amenability and Katz algebras, Algèbres d'opérateurs et leurs applications en physique mathématique, Colloq. Intern. CNRS, t. 274, 1977, p. 451-457. | MR | Zbl

[49] Wassermann (S.). - C*-algebras associated with groups with Kazhdan's property T, Ann. Math., t. 134, 1991, p. 423-431. | MR | Zbl

[50] Woronowicz (S.L.). - Compact matrix pseudogroups, Comm. Math. Phys., t. 111, 1987, p. 613-665. | MR | Zbl

[51] Woronowicz (S.L.). - Twisted SU(2) group. An example of a non commutative calculus, Publ. Res. Inst. Math. Sci., t. 23, 1987, p. 117-181. | MR | Zbl

[52] Woronowicz (S.L.). - Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) group, Invent. Math., t. 93, 1988, p. 35-76. | MR | Zbl

[53] Woronowicz (S.L.). - Unbounded Elements Affiliated with C*-Algebras and Non-Compact Quantum Groups, Comm. Math. Phys., t. 136, 1991, p. 399-432. | MR | Zbl

[54] Woronowicz (S.L.). - Compact quantum groups, preprint.