Purely infinite C * -algebras arising from dynamical systems
Bulletin de la Société Mathématique de France, Tome 125 (1997) no. 2, pp. 199-225.
@article{BSMF_1997__125_2_199_0,
     author = {Anantharaman-Delaroche, Claire},
     title = {Purely infinite $C^\ast $-algebras arising from dynamical systems},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {199--225},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {125},
     number = {2},
     year = {1997},
     doi = {10.24033/bsmf.2304},
     mrnumber = {99i:46051},
     zbl = {0896.46044},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/bsmf.2304/}
}
TY  - JOUR
AU  - Anantharaman-Delaroche, Claire
TI  - Purely infinite $C^\ast $-algebras arising from dynamical systems
JO  - Bulletin de la Société Mathématique de France
PY  - 1997
SP  - 199
EP  - 225
VL  - 125
IS  - 2
PB  - Société mathématique de France
UR  - http://archive.numdam.org/articles/10.24033/bsmf.2304/
DO  - 10.24033/bsmf.2304
LA  - en
ID  - BSMF_1997__125_2_199_0
ER  - 
%0 Journal Article
%A Anantharaman-Delaroche, Claire
%T Purely infinite $C^\ast $-algebras arising from dynamical systems
%J Bulletin de la Société Mathématique de France
%D 1997
%P 199-225
%V 125
%N 2
%I Société mathématique de France
%U http://archive.numdam.org/articles/10.24033/bsmf.2304/
%R 10.24033/bsmf.2304
%G en
%F BSMF_1997__125_2_199_0
Anantharaman-Delaroche, Claire. Purely infinite $C^\ast $-algebras arising from dynamical systems. Bulletin de la Société Mathématique de France, Tome 125 (1997) no. 2, pp. 199-225. doi : 10.24033/bsmf.2304. http://archive.numdam.org/articles/10.24033/bsmf.2304/

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

[2] Aoki (N.), Hiraide (K.). - Topological theory of dynamical systems, Recent advances, North-Holland Mathematical Library, t. 52, 1994. | MR | Zbl

[3] Anantharaman-Delaroche (C.). - Systèmes dynamiques non commutatifs et moyennabilité, Math. Ann., t. 279, 1987, p. 297-315. | MR | Zbl

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

[5] Anantharaman-Delaroche (C.). - Classification des C*-algèbres purement infinies nucléaires, d'après E. Kirchberg, Séminaire Bourbaki 1995-1996, exposé n° 805, to appear in Astérisque, 1996. | Numdam | Zbl

[6] Anantharaman-Delaroche (C.), Renault (J.). - Amenable groupoids, in preparation.

[7] Azurmanian (V.A.), Vershik (A.M.). - Star algebras associated with endomorphisms, in Operator algebras and group representations, vol. I, Pitman, 1984, p. 17-27. | MR | Zbl

[8] Ballmann (W.). - Axial isometries of manifolds of non-positive curvature, Math. Ann., t. 259, 1982, p. 131-144. | MR | Zbl

[9] Ballmann (W.), Gromov (M.), Schroeder (V.). - Manifolds of nonpositive curvature, Progress in Mathematics, t. 61, Birkhäuser, 1985. | MR | Zbl

[10] Bekka (M.), Cowling (M.), De La Harpe (P.). - Some groups whose reduced C*-algebra is simple, Publ. Math. I.H.E.S., t. 80, 1994, p. 117-134. | EuDML | Numdam | MR | Zbl

[11] Benoit (Y.), Labourie (F.). - Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables, Invent. Math., t. 111, 1993, p. 285-308. | EuDML | MR | Zbl

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

[13] Connes (A.). - Sur la théorie non commutative de l'intégration, in Algèbres d'opérateurs, Lecture Notes in Math., Springer-Verlag, t. 725, 1979, p. 19-143. | MR | Zbl

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

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

[16] Deaconu (V.). - Groupoids associated with endomorphisms, Trans. Amer. Math. Soc., t. 347, 1995, p. 1779-1786. | MR | Zbl

[17] Eberlein (P.), O'Neill (B.). - Visibility manifolds, Pacific J. Math., t. 46, 1973, p. 45-110. | MR | Zbl

[18] Fack (T.), Skandalis (G.). - Sur les représentations et idéaux de la C*-algèbre d'un feuilletage, J. Operator Theory, t. 8, 1982, p. 95-129. | MR | Zbl

[19] Ghys (E.), De La Harpe (P.), éd. - Sur les groupes hyperboliques, d'après Mikhael Gromov, Progress in Mathematics, Birkhäuser, t. 83, 1990. | Zbl

[20] Gromov (M.). - Hyperbolic groups, in Essays in group theory, édité par S.M. Gersten, M.S.R.I. Publ., Springer, t. 8, 1987, p. 75-263. | MR | Zbl

[21] Helgason (S.). - Differential geometry, Lie groups, and symmetric spaces. - Academic Press, 1978. | Zbl

[22] Hilsum (M.), Skandalis (G.). - Stabilité des C*-algèbres de feuilletages, Ann. Inst. Fourier, t. 33, 1983, p. 201-208. | EuDML | Numdam | MR | Zbl

[23] Katok (A.), Hasselblatt (B.). - Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its applications, Cambridge University Press, t. 54, 1995. | MR | Zbl

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

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

[26] Lance (E.C.). - Hilbert C*-modules, A toolkit for operator algebraists, London Math. Soc. L. N. S., t. 210, Cambridge University Press, 1995. | MR | Zbl

[27] Mostow (G.D.). - Strong rigidity of locally symmetric spaces. - Princeton University Press, 1973. | MR | Zbl

[28] Muhly (P.), Renault (J.), Williams (D.). - Equivalence and isomorphisms for groupoid C*-algebras, J. Operator Theory, t. 17, 1987, p. 3-22. | MR | Zbl

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

[30] Rieffel (M.A.). - Strong Morita equivalence of certain transformation group C*-algebras, Math. Ann., t. 222, 1976, p. 7-22. | EuDML | MR | Zbl

[31] Shub (M.). - Endomorphisms of compacts differentiable manifolds, Amer. J. Math., t. 91, 1969, p. 175-199. | MR | Zbl

[32] Spatzier (R.J.), Zimmer (R.J.). - Fundamental groups of negatively curved manifolds and actions of semisimple groups, Topology, t. 30, 1991, p. 591-601. | MR | Zbl

[33] Spielberg (J.S.). - Free-product groups, Cuntz-Krieger algebras, and covariant maps, Int. J. Math., t. 2, 1991, p. 457-476. | MR | Zbl

[34] Spielberg (J.S.). - Cuntz-Krieger algebras associated with Fuchsian groups, Ergod. Th. and Dynam. Sys., t. 13, 1993, p. 581-595. | MR | Zbl

[35] Renault (J.). - A groupoid approach to C*-algebras, Lecture Notes in Math. n° 793, Springer-Verlag, New York, Heidelberg, Berlin, 1980. | MR | Zbl

[36] Zimmer (R.J.). - Amenable ergodic group actions and an application to Poisson boundaries of random walk, J. Funct. Anal., t. 27, 1978, p. 350-372. | MR | Zbl

[37] Zimmer (R.J.). - Hyperfinite factors and amenable ergodic actions, Invent. Math., t. 41, 1977, p. 23-31. | MR | Zbl

[38] Zimmer (R.J.). - On the von Neumann algebra of an ergodic group action, Proc. Amer. Math. Soc., t. 66, 1977, p. 289-293. | MR | Zbl

Cité par Sources :