Classification des C * -algèbres purement infinies nucléaires
Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Talk no. 805, p. 7-27
@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},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {241},
     year = {1997},
     note = {talk:805},
     pages = {7-27},
     zbl = {0961.46040},
     mrnumber = {1472533},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1995-1996__38__7_0}
}
Anantharaman-Delaroche, Claire. Classification des $C^\ast $-algèbres purement infinies nucléaires, in Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Talk no. 805, pp. 7-27. http://www.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. | Article | MR 1293309 | Zbl 0838.20042

[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. | Article | MR 438137 | Zbl 0368.46052

[4] B. Blackadar, K -theory for operator algebras, M.S.R.I. Publications 5, Springer Verlag, New York (1986). | Article | MR 859867 | Zbl 0597.46072

[5] B. Blackadar, J. Cuntz, The structure of stable algebraically simple C * - algebras, Amer. J. Math. 104 (1982), 813-822. | Article | MR 667536 | Zbl 0518.46048

[6] B. Blackadar, D. Handelman, Dimension functions and traces on C * - algebras, J. Functional Anal. 45 (1982), 297-340. | Article | MR 650185 | Zbl 0513.46047

[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. | Article | MR 380478 | Zbl 0277.46053

[8] L. G. Brown, R. G. Douglas, P. A. Fillmore, Extensions of C * -algebras and K -homology, Ann. of Math. 105 (1977), 265-324. | Article | MR 458196 | Zbl 0376.46036

[9] M.-D. Choi, A simple C * -algebra generated by two finite order unitaries, Can. J. Math. 31 (1979), 887-890. | MR 540914 | Zbl 0441.46047

[10] M.-D. Choi, E. Effros, Nuclear C * -algebras and the approximation property, Amer. J. Math. 100 (1978), 61-97. | Article | MR 482238 | Zbl 0397.46054

[11] A. Connes, N. Higson, Déformations, morphismes asymptotiques et K -théorie, C. R. Acad. Sci. Paris 310 (1990), 101-106. | MR 1065438 | Zbl 0717.46062

[12] A. Connes, Noncommutative geometry, Academic Press (1994). | MR 1303779 | Zbl 0818.46076

[13] J. Cuntz, Simple C * -algebras generated by isometries, Commun. Math. Phys. 57 (1977), 173-185. | Article | MR 467330 | Zbl 0399.46045

[14] J. Cuntz, Dimension functions on simple C * -algebras, Math. Ann. 233 (1978), 145-153. | Article | MR 467332 | Zbl 0354.46043

[15] J. Cuntz, K -theory for certain C * -algebras, Ann. of Math. 113 (1981), 181-197. | Article | MR 604046 | Zbl 0437.46060

[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. | Article | MR 608527 | Zbl 0461.46047

[17] C. Cuntz, W. Krieger, A class of C * -algebras and topological Markov chains, Invent. Math. 56 (1980), 251-268. | Article | MR 561974 | Zbl 0434.46045

[18] J. Dixmier Les C * -algèbres et leurs représentations, Gauthiers-Villars, Paris (1969). | MR 246136 | Zbl 0174.18601

[19] E. Effros, D. Handelman, C. L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385-407. | Article | MR 564479 | Zbl 0457.46047

[20] G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite dimensional algebras, J. Algebra. 38 (1976), 29-44. | Article | MR 397420 | Zbl 0323.46063

[21] G. A. Elliott, On the classification of C * -algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179-219. | MR 1241132 | Zbl 0809.46067

[22] G. A. Elliott, Are amenable C * -algebras classifiable?, in Representation theory of groups and algebras, Contemporary Mathematics 145 (1993), 423-426. | Article | MR 1216200 | Zbl 0806.46068

[23] G. A. Elliott, The classification problem for amenable C * -algebras, Proc. I.C.M., Zurich (1994). | MR 1403992 | Zbl 0946.46050

[24] T. Fack, K -théorie bivariante de Kasparov, Séminaire Bourbaki, Astérisque 105- 106 (1983), 149-166. | Numdam | MR 728986 | Zbl 0542.46039

[25] U. Haagerup, Quasitraces on exact C * -algebras are traces, Notes manuscrites. | Zbl 1325.46055

[26] G. G. Kasparov, Hilbert C * -modules: theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), 133-150. | MR 587371 | Zbl 0456.46059

[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. | Article | MR 582160 | Zbl 0464.46054

[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 0407.46049

[29] E. Kirchberg, On non-semisplit extensions, tensor products and exactness of group C * -algebras, Invent. Math. 112 (1993), 449-489. | Article | Zbl 0803.46071

[30] E. Kirchberg, On subalgebras of the CAR-algebra, J. Functional Analysis 129 (1995), 35-63. | Article | MR 1322641 | Zbl 0912.46059

[31] E. Kirchberg, Exact C * -algebras, tensor products, and classification of purely infinite algebras, Proc. I.C.M., Zurich (1994). | MR 1403994

[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 1420560 | Zbl 0863.46044

[34] C. Lance, On nuclear C * -algebras, J. Functional Analysis 12 (1973), 157-176. | Article | MR 344901 | Zbl 0252.46065

[35] J. Von Neumann, Charakterisierung des Spectrums eines Integraloperators, Hermann, Paris (1935). | JFM 61.1196.03 | Zbl 0011.30801

[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 0817.46061

[38] M. Rørdam, Classification of certain infinite simple C * -algebras, J. Functional Analysis, à paraître. | Zbl 1016.46037 | Zbl 0831.46063

[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. | Article | MR 894590 | Zbl 0644.46051

[40] M. Takesaki, On the cross norm of the direct product of C * -algebras, Tôhoku Math J. 16 (1964), 111-122. | Article | MR 165384 | Zbl 0127.07302

[41] G. Skandalis, Une notion de nucléarité en K -théorie (d'après J. Cuntz), K - theory 1 (1988), 549-573. | Article | MR 953916 | Zbl 0653.46065

[42] G. Skandalis, Kasparov's bivariant K -theory and applications, Expo. Math. 9 (1991), 193-250. | MR 1121156 | Zbl 0746.19008

[43] G. Skandalis, Le bifoncteur de Kasparov n'est pas exact, C. R. Acad. Sci. Paris 313 (1991), 939-941. | MR 1143449 | Zbl 0744.46066

[44] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roum. Math. Pures et Appl. 21 (1976), 97-113. | MR 415338 | Zbl 0335.46039

[45] S. Wassermann, On tensor products of certain group C * -algebras, J. Functional Analysis 23 (1976), 239-254. | Article | MR 425628 | Zbl 0358.46040

[46] S. Wassermann, Exact C * -algebras and related topics, Lecture Notes Series 19, Seoul National University (1994). | MR 1271145 | Zbl 0828.46054

[47] H. Weyl, Über beschrankte quadratischen Formen deren Differenz vollstetig ist, Rend. Circ. mat. Palermo 27 (1909), 373-392. | Article | JFM 40.0395.01