Purely infinite $C^{*}$-algebras arising from dynamical systems

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1. [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. Zbl0838.20042MR96g:58104
2. [2] AOKI (N.), HIRAIDE (K.). — Topological theory of dynamical systems, Recent advances, North-Holland Mathematical Library, t. 52, 1994. Zbl0798.54047MR95m:58095
3. [3] ANANTHARAMAN-DELAROCHE (C.). — Systèmes dynamiques non commutatifs et moyennabilité, Math. Ann., t. 279, 1987, p. 297-315. Zbl0608.46036MR89f:46127
4. [4] ANANTHARAMAN-DELAROCHE (C.). — C*-algèbres purement infinies et groupes hyperboliques. — Prépublication, Orléans, 1995. 
5. [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. Zbl0961.46040
6. [6] ANANTHARAMAN-DELAROCHE (C.), RENAULT (J.). — Amenable groupoids, in preparation. Zbl0960.43003
7. [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. Zbl0532.46041MR85k:46063
8. [8] BALLMANN (W.). — Axial isometries of manifolds of non-positive curvature, Math. Ann., t. 259, 1982, p. 131-144. Zbl0487.53039MR83i:53068
9. [9] BALLMANN (W.), GROMOV (M.), SCHROEDER (V.). — Manifolds of nonpositive curvature, Progress in Mathematics, t. 61, Birkhäuser, 1985. Zbl0591.53001MR87h:53050
10. [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. Zbl0827.22001MR96a:22020
11. [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. Zbl0777.58029MR94d:58114
12. [12] BLACKADAR (B.), CUNTZ (J.). — The structure of stable algebraically simple C*-algebras, Amer. J. Math., t. 104, 1982, p. 813-822. Zbl0518.46048MR84c:46057
13. [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. Zbl0412.46053MR81g:46090
14. [14] CONNES (A.). — Noncommutative geometry. — Academic Press, 1994. Zbl0818.46076MR95j:46063
15. [15] CUNTZ (J.), KRIEGER (W.). — A class of C*-algebras and topological Markov chains, Invent. Math., t. 56, 1980, p. 251-268. Zbl0434.46045MR82f:46073a
16. [16] DEACONU (V.). — Groupoids associated with endomorphisms, Trans. Amer. Math. Soc., t. 347, 1995, p. 1779-1786. Zbl0826.46058MR95h:46104
17. [17] EBERLEIN (P.), O'NEILL (B.). — Visibility manifolds, Pacific J. Math., t. 46, 1973, p. 45-110. Zbl0264.53026MR49 #1421
18. [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. Zbl0493.46051MR84d:46101
19. [19] GHYS (E.), DE LA HARPE (P.), éd. — Sur les groupes hyperboliques, d'après Mikhael Gromov, Progress in Mathematics, Birkhäuser, t. 83, 1990. Zbl0731.20025
20. [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. Zbl0634.20015MR89e:20070
21. [21] HELGASON (S.). — Differential geometry, Lie groups, and symmetric spaces. — Academic Press, 1978. Zbl0451.53038
22. [22] HILSUM (M.), SKANDALIS (G.). — Stabilité des C*-algèbres de feuilletages, Ann. Inst. Fourier, t. 33, 1983, p. 201-208. Zbl0505.46043MR85f:58115
23. [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. Zbl0878.58020MR96c:58055
24. [24] KIRCHBERG (E.). — The classification of purely infinite C*-algebras using Kasparov's theory, version préliminaire, Humboldt Universität zu Berlin, 1994. 
25. [25] LACA (M.), SPIELBERG (J.). — Purely infinite C*-algebras from boundary actions of discrete groups, Prépublication, 1995. 
26. [26] LANCE (E.C.). — Hilbert C*-modules, A toolkit for operator algebraists, London Math. Soc. L. N. S., t. 210, Cambridge University Press, 1995. Zbl0822.46080MR96k:46100
27. [27] MOSTOW (G.D.). — Strong rigidity of locally symmetric spaces. — Princeton University Press, 1973. Zbl0265.53039MR52 #5874
28. [28] MUHLY (P.), RENAULT (J.), WILLIAMS (D.). — Equivalence and isomorphisms for groupoid C*-algebras, J. Operator Theory, t. 17, 1987, p. 3-22. Zbl0645.46040MR88h:46123
29. [29] PHILLIPS (N.C.). — A classification theorem for purely infinite simple C*-algebras. — Prépublication, Univ. Oregon and Fields Inst., 1995. 
30. [30] RIEFFEL (M.A.). — Strong Morita equivalence of certain transformation group C*-algebras, Math. Ann., t. 222, 1976, p. 7-22. Zbl0328.22013MR54 #7695
31. [31] SHUB (M.). — Endomorphisms of compacts differentiable manifolds, Amer. J. Math., t. 91, 1969, p. 175-199. Zbl0201.56305MR39 #2169
32. [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. Zbl0744.57022MR92m:57047
33. [33] SPIELBERG (J.S.). — Free-product groups, Cuntz-Krieger algebras, and covariant maps, Int. J. Math., t. 2, 1991, p. 457-476. Zbl0769.46044MR92j:46120
34. [34] SPIELBERG (J.S.). — Cuntz-Krieger algebras associated with Fuchsian groups, Ergod. Th. and Dynam. Sys., t. 13, 1993, p. 581-595. Zbl0786.46051MR94k:46143
35. [35] RENAULT (J.). — A groupoid approach to C*-algebras, Lecture Notes in Math. n° 793, Springer-Verlag, New York, Heidelberg, Berlin, 1980. Zbl0433.46049MR82h:46075
36. [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. Zbl0391.28011MR57 #12775
37. [37] ZIMMER (R.J.). — Hyperfinite factors and amenable ergodic actions, Invent. Math., t. 41, 1977, p. 23-31. Zbl0361.46061MR57 #10438
38. [38] ZIMMER (R.J.). — On the von Neumann algebra of an ergodic group action, Proc. Amer. Math. Soc., t. 66, 1977, p. 289-293. Zbl0367.28013MR57 #592

1. Klaus Thomsen, Semi-étale groupoids and applications