Classification des C*-algèbres purement infinies nucléaires

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1. [1] S. Adams, Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups, Topology33 (1994), 765-783. Zbl0838.20042MR1293309
2. [2] C. Anantharaman-Delaroche, C*-algèbres purement infinies et groupes hyperboliques, Prépublication, Université d'Orléans (1995). 
3. [3] W. Arveson, Notes on extensions of C*-algebras, Duke Math. J.44 (1977), 329-355. Zbl0368.46052MR438137
4. [4] B. Blackadar, K-theory for operator algebras, M.S.R.I. Publications5, Springer Verlag, New York (1986). Zbl0597.46072MR859867
5. [5] B. Blackadar, J. Cuntz, The structure of stable algebraically simple C*- algebras, Amer. J. Math.104 (1982), 813-822. Zbl0518.46048MR667536
6. [6] B. Blackadar, D. Handelman, Dimension functions and traces on C*- algebras, J. Functional Anal.45 (1982), 297-340. Zbl0513.46047MR650185
7. [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. Zbl0277.46053MR380478
8. [8] L.G. Brown, R.G. Douglas, P.A. Fillmore, Extensions of C*-algebras and K-homology, Ann. of Math.105 (1977), 265-324. Zbl0376.46036MR458196
9. [9] M.-D. Choi, A simple C*-algebra generated by two finite order unitaries, Can. J. Math.31 (1979), 887-890. Zbl0441.46047MR540914
10. [10] M.-D. Choi, E. Effros, Nuclear C*-algebras and the approximation property, Amer. J. Math.100 (1978), 61-97. Zbl0397.46054MR482238
11. [11] A. Connes, N. Higson, Déformations, morphismes asymptotiques et K-théorie, C. R. Acad. Sci. Paris310 (1990), 101-106. Zbl0717.46062MR1065438
12. [12] A. Connes, Noncommutative geometry, Academic Press (1994). Zbl0818.46076MR1303779
13. [13] J. Cuntz, Simple C*-algebras generated by isometries, Commun. Math. Phys.57 (1977), 173-185. Zbl0399.46045MR467330
14. [14] J. Cuntz, Dimension functions on simple C*-algebras, Math. Ann.233 (1978), 145-153. Zbl0354.46043MR467332
15. [15] J. Cuntz, K-theory for certain C*-algebras, Ann. of Math.113 (1981), 181-197. Zbl0437.46060MR604046
16. [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. Zbl0461.46047MR608527
17. [17] C. Cuntz, W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math.56 (1980), 251-268. Zbl0434.46045MR561974
18. [18] J. DixmierLes C*-algèbres et leurs représentations, Gauthiers-Villars, Paris (1969). Zbl0174.18601MR246136
19. [19] E. Effros, D. Handelman, C.L. Shen, Dimension groups and their affine representations, Amer. J. Math.102 (1980), 385-407. Zbl0457.46047MR564479
20. [20] G.A. Elliott, On the classification of inductive limits of sequences of semi- simple finite dimensional algebras, J. Algebra.38 (1976), 29-44. Zbl0323.46063MR397420
21. [21] G.A. Elliott, On the classification of C*-algebras of real rank zero, J. Reine Angew. Math.443 (1993), 179-219. Zbl0809.46067MR1241132
22. [22] G.A. Elliott, Are amenable C*-algebras classifiable?, in Representation theory of groups and algebras, Contemporary Mathematics145 (1993), 423-426. Zbl0806.46068MR1216200
23. [23] G.A. Elliott, The classification problem for amenable C*-algebras, Proc. I.C.M., Zurich (1994). Zbl0946.46050MR1403992
24. [24] T. Fack, K-théorie bivariante de Kasparov, Séminaire Bourbaki, Astérisque105- 106 (1983), 149-166. Zbl0542.46039MR728986
25. [25] U. Haagerup, Quasitraces on exact C*-algebras are traces, Notes manuscrites. Zbl1325.46055
26. [26] G.G. Kasparov, Hilbert C*-modules: theorems of Stinespring and Voiculescu, J. Operator Theory4 (1980), 133-150. Zbl0456.46059MR587371
27. [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. Zbl0464.46054MR582160
28. [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. Zbl0407.46049
29. [29] E. Kirchberg, On non-semi-split extensions, tensor products and exactness of group C*-algebras, Invent. Math.112 (1993), 449-489. Zbl0803.46071
30. [30] E. Kirchberg, On subalgebras of the CAR-algebra, J. Functional Analysis129 (1995), 35-63. Zbl0912.46059MR1322641
31. [31] E. Kirchberg, Exact C*-algebras, tensor products, and classification of purely infinite algebras, Proc. I.C.M., Zurich (1994). Zbl0897.46057MR1403994
32. [32] E. Kirchberg, The classification of purely infinite C*-algebras using Kasparov's theory , version préliminaire, Humboldt Universität zu Berlin (1994). 
33. [33] M. Laca, J. Spielberg, Purely infinite C*-algebras from boundary actions of discrete groups, Prépublication (1995). Zbl0863.46044MR1420560
34. [34] C. Lance, On nuclear C*-algebras, J. Functional Analysis12 (1973), 157-176. Zbl0252.46065MR344901
35. [35] J. von Neumann, Charakterisierung des Spectrums eines Integraloperators, Hermann, Paris (1935). Zbl0011.30801
36. [36] N.C. Phillips, A classification theorem for purely infinite simple C*-algebras, Prépublication, Univ. Oregon et Fields Inst. (1995). 
37. [37] M. Rørdam, A simple proof of Elliott's result O2 = O2 ⊗ O2, C. R. Math. Rep. Acad. Sci. Canada16 (1994), 31-36. Zbl0817.46061
38. [38] M. Rørdam, Classification of certain infinite simple C*-algebras, J. Functional Analysis, à paraître. Zbl0831.46063
39. [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. Zbl0644.46051MR894590
40. [40] M. Takesaki, On the cross norm of the direct product of C*-algebras, Tôhoku Math J.16 (1964), 111-122. Zbl0127.07302MR165384
41. [41] G. Skandalis, Une notion de nucléarité en K-théorie (d'après J. Cuntz), K- theory1 (1988), 549-573. Zbl0653.46065MR953916
42. [42] G. Skandalis, Kasparov's bivariant K-theory and applications, Expo. Math.9 (1991), 193-250. Zbl0746.19008MR1121156
43. [43] G. Skandalis, Le bifoncteur de Kasparov n'est pas exact, C. R. Acad. Sci. Paris313 (1991), 939-941. Zbl0744.46066MR1143449
44. [44] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roum. Math. Pures et Appl.21 (1976), 97-113. Zbl0335.46039MR415338
45. [45] S. Wassermann, On tensor products of certain group C*-algebras, J. Functional Analysis23 (1976), 239-254. Zbl0358.46040MR425628
46. [46] S. Wassermann, Exact C*-algebras and related topics, Lecture Notes Series19, Seoul National University (1994). Zbl0828.46054MR1271145
47. [47] H. Weyl, Über beschrankte quadratischen Formen deren Differenz vollstetig ist, Rend. Circ. mat. Palermo27 (1909), 373-392. Zbl40.0395.01JFM40.0395.01

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