Topological orbit equivalence and C*-crossed products

Journal fur die Reine und Angewandte Mathematik

Volumn 1995, Issue 469, 1995, Pages 51-112

  Giordano, Thierry ^a   Putnam, Ian F ^b   Skau, Christian F ^c  

^a UNIVERSITY OF OTTAWA   (Canada)

^b UNIVERSITY OF VICTORIA   (Canada)

^c Department of Mathematics and Statistics University of Trondheim AVH ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84941835348     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1995.469.51     Document Type: Article

References (41)

1. B. Blackadar, K-theory for Operator Algebras, Math. Sc. Res. Inst. Publ. 5, Springer-Verlag, Berlin—Heidelberg—New York 1986.
2. B. Blackadar, O. Bratteli, G.A. Elliott and A. Kumjian, Reduction of real rank in inductive limits of C*-algebras, Math. Ann. 292 (1992), 111–126.
3. M. Boyle, Topological orbit equivalence and factor maps in symbolic dynamics, Ph. D. thesis, Univ. of Wash., 1983.
4. M. Boyle, A homeomorphism good on measures and bad on orbits, preprint 1992.
5. M. Boyle and D. Handelman, Entropy versus orbit equivalence for minimal homeomorphisms, Pacific J. Math. 164 (1994), 1–13.
6. M. Boyle, D. Handelman, Orbit equivalence, flow equivalence and ordered cohomology, preprint 1993.
7. O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234.
8. A. Connes, Classification of injective factors, cases II1, II∞, IIIλ, λ≠1, Ann. Math. 104 (1976), 73–115.
9. H. Dye, On groups of measure preserving transformations, I, II, Amer. J. Math. 81 (1959), 119–159; 85 (1963), 551–576.
10. E.G. Effros, Dimensions and C*-algebras, Conf. Board Math. Sci. 46, Amer. Math. Soc., Providence, R.I., 1981.
11. E. Effros, D. Handelman and C.-L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385–407.
12. G.A. Elliott, On the classification of inductive limits of sequences of semisimple finite dimensional algebras, J. Algebra 38 (1976), 29–44.
13. G.A. Elliott, On the classification of C*-algebras of real rank zero, J. reine angew. Math. 443 (1993), 179–219.
14. R. Ellis, Distal transformation groups, Pacific J. Math. 8 (1958), 401–405.
15. L. Fuchs, Infinite abelian groups, Vol. I, Academic Press, New York 1970.
16. K.R. Goodearl, Partially ordered abelian groups with interpolation, Math. surv. monogr. 20, Amer. Math. Soc., Providence, R.I., 1986.
17. U. Haagerup, Connes’ bicentralizer problem and uniqueness of the injective factor of type III1, Acta Math. 158 (1987), 95–148.
18. R.H. Herman, I.F. Putnam and C.F. Skau, Ordered Bratteli diagrams, dimension groups, and topological dynamics, Intern. J. Math. 3 (1992), 827–864.
19. E. Hewitt, K. A. Ross, Abstract Harmonic Analysis I, Grundl. Math. Wiss. 115, Springer Verlag, Berlin 1963.
20. Y. Katznelson, B. Weiss, The classification of non-singular actions revisited, Erg. Th. Dynam. Sys. 11 (1991), 333–348.
21. W. Krieger, On non-singular transformations of a measure space, I, II, Z. Wahrsch. Th. 11 (1969), 83–97; 98–119.
22. W. Krieger, On ergodic flows and isomorphism of factors, Math. Ann. 223 (1976), 19–70.
23. W. Krieger, On a dimension for a class of homeomorphism groups, Math. Ann. 252 (1980), 87–95.
24. K. Kuratowski, Topology, Vol. II, Academic Press, New York 1968.
25. N. Ormes, Strong orbit realization for minimal homeomorphisms, Preliminary manuscript 1955.
26. D. S. Ornstein, D.J. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 262, Amer. Math. Soc., Providence, R.I., 1982.
27. W. Parry, S. Tuncel, Classification problems in ergodic theory, London Math. Soc. Lect. Note Ser. 67, Cambridge University Press, Cambridge, New York 1982.
28. G. Pedersen, C*-algebras and their automorphism groups, Academic Press, New York 1979.
29. K. Petersen, Ergodic theory, Cambridge University Press, Cambridge 1983.
30. K. Petersen, L. Shapiro, Induced flows, Trans. Amer. Math. Soc. 177 (1973), 375–390.
31. I.F. Putnam, The C*-algebras associated with minimal homeomorphisms of the Cantor set, Pacific J. Math. 136 (1989), 329–353.
32. I.F. Putnam, On the topological stable rank of certain transformation group C*-algebras, Ergod. Th. Dynam. Sys. 10 (1990), 197–207.
33. I.F. Putnam, K. Schmidt, C. Skau, C*-algebras associated with Denjoy homeomorphisms of the circle, J. Op. Th. 16 (1986), 99–126.
34. J. Renault, A groupoid approach to C*-algebras, Lect. Notes Math. 793, Springer-Verlag, Berlin—Heidelberg—New York 1980.
35. M. Rieffel, Morita equivalence for operator algebras, Proc. Symp. Pure Math. 38, Part 1 (1982), Amer. Math. Soc., 285–298.
36. H.L. Royden, Real analysis (3rd. edition), Mac Millan, New York 1989.
37. C. Skau, Minimal dynamical systems, ordered Bratteli diagrams and associated C*-crossed products, Current Topics Op. Algs., Proc. Satellite Conf. ICM-90, Nara, Japan (1990), 264–280.
38. S. Stratila, D. Voiculescu, Representations of AF-algebras and of the Group U(∞), Lect. Notes Math. 486, Springer-Verlag, Berlin—Heidelberg—New York 1975.
39. J. Tomiyama, Invitation to C*-algebras and Topological Dynamics, World Sc. Adv. Ser. Dyn. Sys. 3, World Scientific, Singapore 1987.
40. J. Tomiyama, Topological full groups and structure of normalizer in transformation group C*-algebras, Pacific J. Math., to appear.
41. P. Walters, An Introduction to Ergodic Theory, Grad. Texts Math. 79, Springer-Verlag, Berlin—Heidelberg—New York 1982.