Infinite simple C*-algebras and reduced cross products of Abelian C*-algebras and free groups

Manuscripta Mathematica

Volumn 92, Issue 4, 1997, Pages 487-514

  Szymański, Wojciech ^a   Zhang, Shuang ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b UNIVERSITY OF CINCINNATI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040516963     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02678208     Document Type: Article

References (35)

1. Akemann, C. A.; Lee, T.-Y.: Some simple C*-algebras associated with free groups. Indiana Univ. Math. J. 29, 505-511 (1980).
2. Anantharaman-Delaroche, C.: Systèmes dynamiques non commutatifs et moyennabilité. Math. Ann. 279, 297-315 (1987).
3. Brown, L. G.; Pedersen, G. K.: C*-algebras of real rank zero. J. Funct. Anal. 99, 131-149 (1991).
4. Choi, M.-D.: A simple C*-algebra generated by two finite-order unitaries. Canad. J. Math. 31, 867-880 (1979).
5. Choi, M.-D.; Effros, E. G.: Nuclear C*-algebras and injectivity: the general case. Indiana Univ. Math. J. 26, 443-446 (1977).
6. Cuntz, J.: Simple C*-algebras generated by isometries. Comm. Math. Phys. 57, 173-185 (1977).
7. Cuntz, J.: K-theory for certain simple C*-algebras. Ann. of Math. 113, 181-197 (1981).
8. Cuntz, J.; Krieger, W.: A class of C*-algebras and topological Markov chains. Invent. Math. 56, 251-268 (1980).
9. Elliott, G. A.: A classification of certain simple C*-algebras. J. reine angew. Math. 443, 179-219 (1993).
10. Elliott, G. A.; Gong, G.: On the classification of C*-algebras of real rank zero, II. Ann. of Math. 144, 497-610 (1996).
11. Elliott, G. A.; Rørdam, M.: Classification of certain infinite simple C*-algebras, II. Comment. Math. Helv. 70, 615-638 (1995).
12. Enomoto, M.; Takehana, H.; Watatani, Y.: C*-algebras on free semi-groups as extensions of Cuntz algebras. Math. Japonica 24, 527-531 (1980).
13. Figà-Talamanca, A.; Nebbia, C.: Harmonic analysis and representation theory for groups acting on homogeneous trees. (London Math. Soc. Lecture Notes Ser. 162): Cambridge Univ. Press, 1991.
14. Gromov, M.: Hyperbolic groups. (Essays in group theory, ed. Gersten, S. M.: MSRI Publ. no 8) Berlin Heidelberg New York: Springer, 1987.
15. Handelman, D.; Yin, H.-S.: Toeplitz extensions and automorphisms affiliated with linear characters of groups. Bull. London Math. Soc. 20, 54-60 (1988).
16. de la Harpe, P.: Operator algebras, free groups and other groups. Astérisque 232, 121-153 (1995).
17. de la Harpe, P.; Skandalis, G.: Powers property and simple C*-algebras. Math. Ann. 273, 241-250 (1986).
18. Kadison, R V.; Ringrose, J. R: Fundamentals of the theory of operator algebras, (vol. II): Academic Press, 1986.
19. Kirchberg, E.: The classification of purely infinite C*-algebras using Kasparov's theory, draft.
20. Laca, M.; Spielberg, J.: Purely infinite C*-algebras from boundary actions of discrete groups. J. reine angew. Math. 480, 125-139 (1996).
21. Lance, E. C.: Tensor products and nuclear C*-algebras. Proc. Symposia in Pure Math. 38, 379-399 (1982).
22. Lin, H.; Phillips, N. C.: Classification of direct limits of even Cuntz-circle algebras. Mem. Amer. Math. Soc. 118, 1995.
23. Murphy, G. J.: C*-algebras and operator theory. Academic Press, 1991.
24. Paschke, W. L.; Salinas, N.: C*-algebras associated with free products of groups. Pac. J. Math. 82, 211-221 (1979).
25. Pask, D.; Raeburn, I.: On the K-theory of Cuntz-Krieger algebras. Publ. Res. Inst. Math. Sci. 32, 415-443 (1996).
26. Pedersen, G. K.: C*-algebras and their automorphism groups. Academic Press, 1979.
27. Phillips, N. C.: Classification of purely infinite simple C*-algebras, draft.
28. Robertson, G.; Steger, T.: C*-algebras arising from group actions on the boundary of a triangle building. Proc. London Math. Soc. (3) 72, 613-637 (1996).
29. Rørdam, M.: Classification of inductive limits of Cuntz algebras. J. reine angew. Math. 440, 175-200 (1993).
30. Spielberg, J.: Free product groups, Cuntz-Krieger algebras, and covariant maps. Internat. J. Math. 2, 457-476 (1991).
31. Su, H.: On the classification of C*-algebras of real rank zero: Inductive limits of matrix algebras over non-Hausdorff graphs. Mem. Amer. Math. Soc. 114, 1995.
32. ∞ factors generated by purely infinite simple C*-algebras associated with free groups, preprint.
33. Zhang, S.: A property of purely infinite simple C*-algebras. Proc. Amer. Math. Soc. 109, 717-720 (1990).
34. Zhang, S.: Purely infinite simple C*-algebras arising from reduced group C*-algebras, preprint.
35. n, preprint.