Classification des C * -algèbres purement infinies nucléaires
Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 805, 21 p.
@incollection{SB_1995-1996__38__7_0,
     author = {Anantharaman-Delaroche, Claire},
     title = {Classification des $C^\ast $-alg\`ebres purement infinies nucl\'eaires},
     booktitle = {S\'eminaire Bourbaki : volume 1995/96, expos\'es 805-819},
     series = {Ast\'erisque},
     note = {talk:805},
     pages = {7--27},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {241},
     year = {1997},
     mrnumber = {1472533},
     zbl = {0961.46040},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1995-1996__38__7_0/}
}
TY  - CHAP
AU  - Anantharaman-Delaroche, Claire
TI  - Classification des $C^\ast $-algèbres purement infinies nucléaires
BT  - Séminaire Bourbaki : volume 1995/96, exposés 805-819
AU  - Collectif
T3  - Astérisque
N1  - talk:805
PY  - 1997
SP  - 7
EP  - 27
IS  - 241
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1995-1996__38__7_0/
LA  - fr
ID  - SB_1995-1996__38__7_0
ER  - 
%0 Book Section
%A Anantharaman-Delaroche, Claire
%T Classification des $C^\ast $-algèbres purement infinies nucléaires
%B Séminaire Bourbaki : volume 1995/96, exposés 805-819
%A Collectif
%S Astérisque
%Z talk:805
%D 1997
%P 7-27
%N 241
%I Société mathématique de France
%U http://archive.numdam.org/item/SB_1995-1996__38__7_0/
%G fr
%F SB_1995-1996__38__7_0
Anantharaman-Delaroche, Claire. Classification des $C^\ast $-algèbres purement infinies nucléaires, dans Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 805, 21 p. http://archive.numdam.org/item/SB_1995-1996__38__7_0/

[1] S. Adams, Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups, Topology 33 (1994), 765-783. | DOI | MR | Zbl

[2] C. Anantharaman-Delaroche, C * -algèbres purement infinies et groupes hyperboliques, Prépublication, Université d'Orléans (1995).

[3] W. Arveson, Notes on extensions of C * -algebras, Duke Math. J. 44 (1977), 329-355. | DOI | MR | Zbl

[4] B. Blackadar, K -theory for operator algebras, M.S.R.I. Publications 5, Springer Verlag, New York (1986). | DOI | MR | Zbl

[5] B. Blackadar, J. Cuntz, The structure of stable algebraically simple C * - algebras, Amer. J. Math. 104 (1982), 813-822. | DOI | MR | Zbl

[6] B. Blackadar, D. Handelman, Dimension functions and traces on C * - algebras, J. Functional Anal. 45 (1982), 297-340. | DOI | MR | Zbl

[7] L. G. Brown, R. G. Douglas, P. A. Fillmore, Unitary equivalence modulo the compact operators and extensions of C * -algebras, Proc. Conf. on Operator Theory, Springer Lecture Notes in Math. 345 (1973), 58-128. | DOI | MR | Zbl

[8] L. G. Brown, R. G. Douglas, P. A. Fillmore, Extensions of C * -algebras and K -homology, Ann. of Math. 105 (1977), 265-324. | DOI | MR | Zbl

[9] M.-D. Choi, A simple C * -algebra generated by two finite order unitaries, Can. J. Math. 31 (1979), 887-890. | MR | Zbl

[10] M.-D. Choi, E. Effros, Nuclear C * -algebras and the approximation property, Amer. J. Math. 100 (1978), 61-97. | DOI | MR | Zbl

[11] A. Connes, N. Higson, Déformations, morphismes asymptotiques et K -théorie, C. R. Acad. Sci. Paris 310 (1990), 101-106. | MR | Zbl

[12] A. Connes, Noncommutative geometry, Academic Press (1994). | MR | Zbl

[13] J. Cuntz, Simple C * -algebras generated by isometries, Commun. Math. Phys. 57 (1977), 173-185. | DOI | MR | Zbl

[14] J. Cuntz, Dimension functions on simple C * -algebras, Math. Ann. 233 (1978), 145-153. | DOI | EuDML | MR | Zbl

[15] J. Cuntz, K -theory for certain C * -algebras, Ann. of Math. 113 (1981), 181-197. | DOI | MR | Zbl

[16] J. Cuntz, A class of C * -algebras and topological Markov chains II : Reducible chains and the Ext-functor for C * -algebras, Invent. Math. 63 (1981), 25-40. | DOI | EuDML | MR | Zbl

[17] C. Cuntz, W. Krieger, A class of C * -algebras and topological Markov chains, Invent. Math. 56 (1980), 251-268. | DOI | EuDML | MR | Zbl

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

[19] E. Effros, D. Handelman, C. L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385-407. | DOI | MR | Zbl

[20] G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite dimensional algebras, J. Algebra. 38 (1976), 29-44. | DOI | MR | Zbl

[21] G. A. Elliott, On the classification of C * -algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179-219. | EuDML | MR | Zbl

[22] G. A. Elliott, Are amenable C * -algebras classifiable?, in Representation theory of groups and algebras, Contemporary Mathematics 145 (1993), 423-426. | DOI | MR | Zbl

[23] G. A. Elliott, The classification problem for amenable C * -algebras, Proc. I.C.M., Zurich (1994). | MR | Zbl

[24] T. Fack, K -théorie bivariante de Kasparov, Séminaire Bourbaki, Astérisque 105- 106 (1983), 149-166. | EuDML | Numdam | MR | Zbl

[25] U. Haagerup, Quasitraces on exact C * -algebras are traces, Notes manuscrites. | Zbl

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

[27] G. G. Kasparov, The operator K -functor and extensions of C * -algebras , Math. U.S.S.R. Izv. 16 (1981), 513-572. Traduit de Izv. Acad. Nauk S.S.S.R., Ser. Math. 44 (1980), 571-636. | DOI | MR | Zbl

[28] E. Kirchberg, Positive maps and C * -nuclear algebras, Proc. Intern. Conf. on Operator Algebras, Ideals and their applications in theoretical Physics, Leipzig (1977), 225-257, Teubner, Leipzig, 1978. | Zbl

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

[30] E. Kirchberg, On subalgebras of the CAR-algebra, J. Functional Analysis 129 (1995), 35-63. | DOI | MR | Zbl

[31] E. Kirchberg, Exact C * -algebras, tensor products, and classification of purely infinite algebras, Proc. I.C.M., Zurich (1994). | MR

[32] E. Kirchberg, The classification of purely infinite C * -algebras using Kasparov's theory , version préliminaire, Humboldt Universität zu Berlin (1994).

[33] M. Laca, J. Spielberg, Purely infinite C * -algebras from boundary actions of discrete groups, Prépublication (1995). | MR | Zbl

[34] C. Lance, On nuclear C * -algebras, J. Functional Analysis 12 (1973), 157-176. | DOI | MR | Zbl

[35] J. Von Neumann, Charakterisierung des Spectrums eines Integraloperators, Hermann, Paris (1935). | JFM | Zbl

[36] N. C. Phillips, A classification theorem for purely infinite simple C * -algebras, Prépublication, Univ. Oregon et Fields Inst. (1995).

[37] M. Rørdam, A simple proof of Elliott's result 𝒪 2 = 𝒪 2 𝒪 2 , C. R. Math. Rep. Acad. Sci. Canada16 (1994), 31-36. | Zbl

[38] M. Rørdam, Classification of certain infinite simple C * -algebras, J. Functional Analysis, à paraître. | Zbl

[39] J. Rosenberg, C. Schochet, The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K -functor, Duke J. Math. 55 (1987), 431-474. | DOI | MR | Zbl

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

[41] G. Skandalis, Une notion de nucléarité en K -théorie (d'après J. Cuntz), K - theory 1 (1988), 549-573. | DOI | MR | Zbl

[42] G. Skandalis, Kasparov's bivariant K -theory and applications, Expo. Math. 9 (1991), 193-250. | MR | Zbl

[43] G. Skandalis, Le bifoncteur de Kasparov n'est pas exact, C. R. Acad. Sci. Paris 313 (1991), 939-941. | MR | Zbl

[44] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roum. Math. Pures et Appl. 21 (1976), 97-113. | MR | Zbl

[45] S. Wassermann, On tensor products of certain group C * -algebras, J. Functional Analysis 23 (1976), 239-254. | DOI | MR | Zbl

[46] S. Wassermann, Exact C * -algebras and related topics, Lecture Notes Series 19, Seoul National University (1994). | MR | Zbl

[47] H. Weyl, Über beschrankte quadratischen Formen deren Differenz vollstetig ist, Rend. Circ. mat. Palermo 27 (1909), 373-392. | DOI | JFM