@article{BSMF_1996__124_1_141_0, author = {Blanchard, Etienne}, title = {D\'eformations de $C^\ast $-alg\`ebres de {Hopf}}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {141--215}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {124}, number = {1}, year = {1996}, doi = {10.24033/bsmf.2278}, mrnumber = {97f:46092}, zbl = {0851.46040}, language = {fr}, url = {http://www.numdam.org/articles/10.24033/bsmf.2278/} }
TY - JOUR AU - Blanchard, Etienne TI - Déformations de $C^\ast $-algèbres de Hopf JO - Bulletin de la Société Mathématique de France PY - 1996 SP - 141 EP - 215 VL - 124 IS - 1 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/bsmf.2278/ DO - 10.24033/bsmf.2278 LA - fr ID - BSMF_1996__124_1_141_0 ER -
%0 Journal Article %A Blanchard, Etienne %T Déformations de $C^\ast $-algèbres de Hopf %J Bulletin de la Société Mathématique de France %D 1996 %P 141-215 %V 124 %N 1 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/bsmf.2278/ %R 10.24033/bsmf.2278 %G fr %F BSMF_1996__124_1_141_0
Blanchard, Etienne. Déformations de $C^\ast $-algèbres de Hopf. Bulletin de la Société Mathématique de France, Volume 124 (1996) no. 1, pp. 141-215. doi : 10.24033/bsmf.2278. http://www.numdam.org/articles/10.24033/bsmf.2278/
[1] Thèse, Université Pierre et Marie Curie, Paris, 1980.
. -[2] Représentation régulière du groupe quantique Eμ(2) de Woronowicz, C. R. Acad. Sci. Paris, t. 314, 1992, p. 1021-1026. | MR | Zbl
. -[3] Représentation régulière du groupe quantique des déplacements de Woronowicz, preprint.
. -[4] 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
et . -[5] Mappings between function spaces, Trans. Amer. Math. Soc., t. 72, 1952, p. 400-413. | MR | Zbl
and . -[6] Déformation du groupe de Lie-Poisson SU(2), prépublication n° 13 de l'URA 1408, Toulouse, 1992.
. -[7] RKK(X)-nucléarité (d'après G. Skandalis), preprint.
. -[8] K-theory for Operator Algebras, Math. Sci. Res. Inst. Publ., t. 5, 1986. | MR | Zbl
. -[9] Représentations de champs de C*-algèbres, C.R. Acad. Sci. Paris, t. 314, 1992, p. 911-914. | MR | Zbl
. -[10] Espace vectoriels topologiques. - Hermann et Cie, Paris, 1955.
. -[11] Nuclear C*-algebras and injectivity : the general case, Indiana Univ. Math. J., t. 26, 1977, p. 443-446. | MR | Zbl
and . -[12] Factorization in group algebras, Duke Math. J., t. 26, 1959, p. 199-205. | MR | Zbl
. -[13] Classification of injective factors, Ann. of Math., t. 104, 1976, p. 73-115. | MR | Zbl
. -[14] Les C*-algèbres et leurs représentations. - Gauthiers-Villars, Paris, 1969. | MR | Zbl
. -[15] Quantum groups. - Proceedings of the I.C.M., Berkeley, California, 1986.
. -[16] The classification and structure of C*-algebra bundles, Mem. Amer. Math. Soc., t. 222, 1979. | MR | Zbl
. -[17] Tensor products of operator algebras, Adv. in Math., t. 25, 1977, p. 1-34. | MR | Zbl
and . -[18] The Heisenberg Group and K-Theorie, K-Theory, t. 7, 1993, p. 409-428. | MR | Zbl
, and . -[19] Une dualité dans les algèbres de von Neumann, Mémoire Soc. Math. France, suppl. Bull., n° 44, 1975, p. 1-144. | Numdam | MR | Zbl
et . -[20] Algèbres de Kac moyennables, Pacific J. Math., t. 125, 2, 1986, p. 363-379. | MR | Zbl
et . -[21] The structure of algebras of operator fields, Acta Math., t. 106, 1962, p. 237-268. | Zbl
. -[22] On the embedding of normed rings into the ring of operators in Hilbert space, Mat. Sb., t. 12, 1943, p. 197-213. | Zbl
and . -[23] The local structure of twisted covariance algebras, Acta Math., t. 140, 1978, p. 191-250. | MR | Zbl
. -[24] La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque n° 175, 1989.
et . -[25] 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] Hilbert C*-modules : theorems of Stinespring aand Voiculescu, J. Operator Theory, t. 4, 1980, p. 133-150. | MR | Zbl
. -[27] Equivariant KK-theory and the Novikov conjecture, Invent. Math., t. 91, 1988, p. 147-201. | MR | Zbl
. -[28] Takesaki's duality for a non degenerate coaction, Math. Scand., t. 55, 1985, p. 141-151. | MR | Zbl
. -[29] On non-semisplit extension, tensor products and exactness of group C*-algebras, Invent. Math., t. 112, 1993, p. 449-489. | MR | Zbl
. -[30] Operations on continuous bundles of C*-algebras, preprint.
and . -[31] Tensor product and nuclear C*-algebras, Operator Algebras and Applications, Proc. Sympos. Pure Math., t. 38, I, 1982, p. 379-399. | MR | Zbl
. -[32] On the C*-algebras of operator fields, Indiana Univ. Math. J., t. 25, 1976, p. 303-314. | MR | Zbl
. -[33] Representations of quantum groups and a q-analogue of orthogonal polynomials, C. R. Acad. Sci. Paris, t. 307, 1988, p. 559-564. | MR | Zbl
, , , and . -[34] Continuous selection I, Ann. Math., t. 63, 1956, p. 361-382. | MR | Zbl
. -[35] A framework for deformation quantization, thesis, Berkeley, 1992.
. -[36] On the Haar measure of the quantum SU(N) group, Comm. Math. Phys., t. 153, 1993, p. 217-228. | MR | Zbl
. -[37] Inner product modules over B*-algebras, Trans. Amer. Math. Soc., t. 182, 1973, p. 443-468. | MR | Zbl
. -[38] C*-algebras and their automorphism groups. - Academic press, 1979. | MR | Zbl
. -[39] Quantum deformation of Lorentz group, Comm. Math. Phys., t. 130, 1990, p. 381-431. | MR | Zbl
and . -[40] Continuous fields of C*-algebras coming from group cocycles and actions, Math. Ann., t. 283, 1989, p. 631-643. | MR | Zbl
. -[41] Deformation quantization of Heisenberg manifolds, Comm. Math. Phys., t. 122, 1989, p. 531-562. | MR | Zbl
. -[42] 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] Operator algebras and duality, Proc. Intern. Congr. Math., t. 2, 1990, p. 997-1009. | MR | Zbl
. -[44] Modular theory in operator algebras. - Academiei and Abacus Press, 1981. | MR | Zbl
. -[45] On the cross norm of the direct product of C*-algebras, Tôhoku Math. J., t. 16, 1964, p. 111-122. | MR | Zbl
. -[46] Topological representation of C*-algebras, Tôhoku Math. J., t. 14, 1962, p. 187-204. | MR | Zbl
. -[47] C*-algèbres de Hopf et C*-algèbres de Kac, Proc. London Math. Soc. (3), t. 50, 1985, p. 131-174. | MR | Zbl
. -[48] 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] C*-algebras associated with groups with Kazhdan's property T, Ann. Math., t. 134, 1991, p. 423-431. | MR | Zbl
. -[50] Compact matrix pseudogroups, Comm. Math. Phys., t. 111, 1987, p. 613-665. | MR | Zbl
. -[51] 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] Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) group, Invent. Math., t. 93, 1988, p. 35-76. | MR | Zbl
. -[53] Unbounded Elements Affiliated with C*-Algebras and Non-Compact Quantum Groups, Comm. Math. Phys., t. 136, 1991, p. 399-432. | MR | Zbl
. -[54] Compact quantum groups, preprint.
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