Classification des $C^\ast $-algèbres purement infinies nucléaires

Classification des

C^{*}

-algèbres purement infinies nucléaires

Anantharaman-Delaroche, Claire

Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 805, 21 p.

EuDML MR Zbl | 3 citations dans Numdam

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     author = {Anantharaman-Delaroche, Claire},
     title = {Classification des $C^\ast $-alg\`ebres purement infinies nucl\'eaires},
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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.. https://www.numdam.org/item/SB_1995-1996__38__7_0/

Bibliographie
Cité par

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

[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. | Zbl | MR | DOI

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

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

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

[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. | Zbl | MR | DOI

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

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

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

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

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

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

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

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

[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. | Zbl | MR | EuDML | DOI

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

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

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

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

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

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

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

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

[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. | Zbl | MR

[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. | Zbl | MR | DOI

[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. | Zbl | EuDML | DOI

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

[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. | Zbl | MR | DOI

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

[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 $𝒪_{2} = 𝒪_{2} \otimes 𝒪_{2}$ , 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. | Zbl | MR | DOI

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

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

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

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

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

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

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

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