On a class of type II1 factors with Betti numbers invariants

Annals of Mathematics

Volumn 163, Issue 3, 2006, Pages 809-899

  Popa, Sorin ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748706181     PISSN: 0003486X     EISSN: 0003486X     Source Type: Journal    
DOI: 10.4007/annals.2006.163.809     Document Type: Article

References (78)

1. [A-De] C. ANANTHARAM-DELAROCHE, On Connes' property (T) for von Neumann algebras, Math. Japon. 32 (1987), 337-355.
2. [At] M. ATIYAH, Elliptic operators, discrete groups and von Neumann algebras, in Colloque "Analyse et Topologie", en l'Honneur de Henri, Cartan (Orsay, 1974), Astérisque 32, 43-72, Soc. Math. France, Paris, 1976.
3. [Bi] D. BISCH, A note on intermediate subfactors, Pacific J. Math. 163 (1994), 201-216.
4. [Bo] F. BOCA, On the method of constructing irreducible finite index subfactors of Popa, Pacific J. Math. 161 (1993), 201-231.
5. 2-cohomology of negatively curved Riemannian symmetric spaces, Ann. Acad. Sci. Fenn. Ser. A Math. 10 (1985), 95-105.
6. [Bu] M. BURGER, Kazhdan constants for SL(3, ℤ), J. Reine. Angew. Math. 413 (1991), 36-67.
7. [dCaH] J. DE CANNIÉRE and U. HAAGERUP, Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups, Amer. J. Math. 107 (1984), 455-500.
8. 2-cohomology and group cohomology, Topology 25 (1986), 189-215.
9. [CCJJV] P.-A. CHERIX, M. COWLING, P. JOLISSAINT, P. JULG, and A. VALETTE, Groups with the Haagerup Property (Gromov's a-T-menability), Progr. in Math. 197, Birkhäuser Verlag, Basel, 2001.
10. [Cho] M. CHODA, Group factors of the Haagerup type, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), 174-177.
11. [Chr] E. CHRISTENSEN, Subalgebras of a finite algebra, Math. Ann. 243 (1979), 17-29.
12. 1 with countable fundamental group, J. Operator Theory 4 (1980), 151-153.
13. [C2] _, Classification of injective factors, Ann. of Math. 104 (1976), 73-115.
14. [C3] _, Classification des facteurs, Proc. Sympos. Pure Math. 38 (1982), 43-109.
15. [C4] _, Sur la théorie non commutative de l'intégration, in Algèbres d'Opérateurs (Scin. Les Plans-sur-Bex, 1978), 19-143, Lecture. Notes in Math. 725, SpringerVerlag, New York, 1979.
16. [C5] _, Sur la classification des facteurs de type II, C. R. Acad. Sci. Paris Sér. I Math. 281 (1975), A13-A15.
17. [C6] _, Factors and geometry, lecture at MSRI, May 1, 2001.
18. [C7] _, Correspondences, handwritten notes, 1980.
19. [CJ] A. CONNES and V. F. R. JONES, Property (T) for von Neumann algebras, Bull. London Math. Soc. 17 (1985), 57-62.
20. [CW] A. CONNES and B. WEISS, Property T and asymptotically invariant sequences, Israel J. Math. 37 (1980), 209-210.
21. [CowH] M. COWLING and U. HAAGERUP, Completely bounded multipliers and the Fourier algebra of a simple Lie group of real rank one, Invent. Math. 96 (1989), 507-549.
22. [DeKi] C. DELAROCHE and A. KIRILLOV, Sur les relations entre l'espace dual d'un groupe et la structure de ses sous-groupes fermés, Sém. Bourbaki 10, Exp. No. 343, 507-528, Soc. Math. France, Paris, 1995.
23. [D] J. DIXMIER, Sous-anneaux abéliens maximaux dans les facteurs de type fini, Ann. of Math. 59 (1954), 279-286.
24. [Dy] H. DYE, On groups of measure-preserving transformations, I, II, Amer. J. Math. 81 (1959), 119-159,
25. and H. DYE, On groups of measure-preserving transformations, I, II, Amer. J. Math. 85 (1963), 551-576.
26. [Dyk] K. DYKEMA, Interpolated free group factors, Pacific J. Math. 163 (1994), 123-135.
27. [Ey] P. EYMARD, Moyennes Invariantes et Représentations Unitaires, Lecture Notes in Math. 300, Springer-Verlag, New York, 1972.
28. [FM] J. FELDMAN and C. C. MOORE, Ergodic equivalence relations, cohomology, and von Neumann algebras I, II, Trans. Amer. Math. Soc. 234 (1977), 289-324, 325-359.
29. [Fu] A. FURMAN, Gromov's measure equivalence and rigidity of higher rank lattices, Ann. of Math. 150 (1999), 1059-1081.
30. [G1] D. GABORIAU, Coût des rélations d'équivalence et des groupes, Invent. Math. 139 (2000), 41-98.
31. 2 de relations d'équivalence et de groupes, Publ. Math. IHES 95 (2002), 93-150.
32. [Ge] L. GE, Prime factors, Proc. Natl. Acad. Sci. USA 93 (1996), 12762-12763.
33. [GoNe] V. Y. GOLODETS and N. I. NESSONOV, T-property and nonisomorphic full factors of type II and III, J. Fund. Anal. 70 (1987), 80-89.
34. [Gr] M. GROMOV, Rigid transformation groups, in Géométrie Différentielle (Paris 1986), 65-139, Travaux en Cours 33, Hermann, Paris, 1988.
35. [H] U. HAAGERUP, An example of a, nonnuclear C*-algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293.
36. [dHVa] P. DE LA HARPE and A. VALETTE, La propriété T de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France, Paris (1989).
37. [Hj] G. HJORTH, A lemma for cost attained, UCLA preprint, 2002.
38. [HkS] R. HOEGH-KROHN and T. SKJELBRED, Classification of C*-algebras admitting ergodic actions of the two-dimensional torus, J. Reine Angew. Math. 328 (1981), 1-8.
39. [ILP] M. IZUMI, R. LONGO, and S. POPA, A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras, J. Funct. Anal. 155 (1998), 25-63.
40. [Jo1] P. JOLISSAINT, Haagerup approximation property for finite von Neumann algebras, J. Operator Theory 48 (2002), 549-571.
41. [Jo2] _, On the property (T) for pairs of topological groups, Enseign. Math. 51 (2005), 31-45.
42. [J1] V. F. R. JONES, Index for subfactors, Invent. Math. 72 (1983), 1-25.
43. [J2] _, A converse to Ocneanu's theorem, J. Operator Theory 10 (1983), 61-63.
44. [JPo] V. F. R. JONES and S. POPA, Some properties of MASAs in factors, in Invariant Subspaces and other Topics (Timişoara/Herculane, 1981), Operator Theory. Adv. Appl. 6 (1982), 89-102, Birkhäuser, Boston, MA, 1982.
45. [K1] R. V. KADISON, Problems on von Neumann algebras, Baton Rouge Conference, 1967.
46. [K2] _, Diagonalizing matrices, Amer. Math. J. 106 (1984), 1451-1468.
47. [KafW] V. KAFTAL and G. WEISS, Compact derivations relative to semifinite von Neumann algebras, J. Funct. Anal. 62 (1985), 202-220.
48. [Ka] D. KAZHDAN, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl. 1 (1967), 63-65.
49. [KoY] H. KOSAKI and S. YAMAGAMI, Irreducible bimodules associated with crossed product algebras, Internat. J. Math. 3 (1992), 661-676.
50. 2-Euler characteristics and Burnside groups, J. Reine Angew. Math. 496 (1998), 213-236.
51. [Ma] G. MARGULIS, Finitely-additive invariant measures on Euclidian spaces, Ergodic Theory Dynam. Systems 2 (1982), 383-396.
52. [McD] D. McDuFF, Central sequences and the hyperfinite factor, Proc. London Math. Soc. 21 (1970), 443-461.
53. [MvN] F. MURRAY and J. VON NEUMANN, On rings of operators. IV, Ann. of Math. 44 (1943), 716-808.
54. [PiPo] M. PIMSNER and S. POPA, Entropy and index for subfactors, Ann. Sci. École Norm. Sup. 19 (1986), 57-106.
55. [Pol] S. POPA, Correspondences, INCHEST preprint 1986, unpublished.
56. [Po2] _, Classification of Subfactors and their Endomorphisms, CBMS Lecture Notes Series in Math. 86 (1994), A. M. S., Providence, RI, 1995.
57. [Po3] _, Classification of amenable subfactors of type II, Acta Math. 172 (1994), 163-255.
58. [Po4] _, Free independent sequences in type Hi factors and related problems, in Recend Advances in Operator Algebras (Orléans 1992), Astérisque 232 (1995), 187-202.
59. [Po5] S. POPA, Some properties of the symmetric enveloping algebra of a subfactor with applications to amenability and property T, Doc. Math. 4 (1999), 665-744.
60. [Po6] _, On a problem of R. V. Kadison on maximal abelian *-subalgebras in factors, Invent. Math. 65 (1981), 269-281.
61. [Po7] _, The relative Dixmier property for inclusions of von Neumann algebras of finite index, Ann. Sci. École Norm. Sup. 32 (1999), 743-767.
62. 1 factors, Math. Scand. 57 (1985), 171-188.
63. 1 factors, in Mathematical Physics in Mathematics and Physics (Siena, 2000), Fields Inst Commun. 30, 321-324, A. M. S., Providence, RI, 2001.
64. [PoRa] S. POPA and F. RADULESCU, Derivations of von Neumann algebras into the compact ideal space of a semifmite algebra, Duke Math. J. 57 (1988), 485-518.
65. 1 factors, Math. Scand. 92 (2003), 93-102.
66. [Ra] F. RADULESCU, Random matrices, amalgamated free products and subfactors of the von Neumann algebra, of a free group of noninteger index, Invent. Math. 115 (1994), 347-389.
67. [Ri] M. RIEFFEL, C*-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), 415-429.
68. [S] S. SAKAI, C*-Algebras and W*-Algebras, Springer-Verlag, New York, 1971.
69. [Sa] J.- L. SAUVAGEOT, Sur le produit tensoriel relatif d'espaces de Hubert, J. Operator Theory 9 (1983), 237-252.
70. [Sc] K. SCHMIDT, Asymptotically invariant sequences and an action of SL(2, ℤ) on the 2-sphere, Israel J. Math. 37 (1980), 193-208.
71. [Sha] Y. SHALOM, Bounded generation and Kazhdan's property (T), Publ. Math. I.H.E.S. 90 (2001), 145-168.
72. [Sh] D. SHLYAKHTENKO, Free quasi-free states, Pacific J. Math. 177 (1997), 329-368.
73. [Si] I. M. SINGER, Automorphisms of finite factors, Amer. J. Math. 77 (1955), 117-133.
74. [Va] A. VALETTE, Group pairs with the relative property (T) from arithmetic lattices, Geom. Dedicata 112 (2005), 183-196.
75. [V1] D. Voiculescu, Circular and semicircular systems and free product factors, Progr. in Math. 92, Birkhauser, Boston, 1990, 45-60.
76. [V2] _, The analogues of entropy and of Fisher's information measure in free probability. II, Invent. Math. 118 (1994), 411-440.
77. [W] A. Wassermann, Coactions and Yang-Baxter equations for ergodic actions and subfactors, London Math. Soc. Lecture Note Series 136, Cambridge Univ. Press, Cambridge, 1988, 203-236.
78. [Zi] R. Zimmer, Ergodic Theory and Semisimple Groups, Birkhaüser-Verlag, Boston, 1984.