Cuntz-pimsner algebras of group actions

Journal of Operator Theory

Volumn 52, Issue 2, 2004, Pages 223-249

  Nekrashevych, Volodymyr V ^a  

^a JACOBS UNIVERSITY BREMEN   (Germany)

Author keywords

Bimodules; Cuntz algebras; Cuntz Pimsner algebras; Grigorchuk group; Higman Thompson groups; One sided shift; Self similar group actions

Indexed keywords

EID: 15744383940     PISSN: 03794024     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. L. BARTHOLDI, R.I. GRIGORCHUK, Lie methods in growth of groups and groups of finite width, in Computational and Geometric Aspects of Modern Algebra, London Math. Soc. Lecture Note Ser., vol. 275, Cambridge Univ. Press, Cambridge 2000, pp.1-27.
2. L. BARTHOLDI, R.I. GRIGORCHUK, On the spectrum of Hecke type operators related to some fractal groups, [English], in Proc. Steklov Inst. Math. 231(2000), 1-41.
3. L. BARTHOLDI, R.I. GRIGORCHUK, On parabolic subgroups and Hecke algebras of some fractal groups, Serdica Math. J. 28(2002), 47-90.
4. O. BRATELLI, P.E.T. JORGENSEN, Iterated function systems and permutation representations of the Cuntz algebra, Mem, Amer. Math. Soc. 663(1999).
5. A.M. BRUNNER, S.N. SIDKI, A.C. VIEIRA, A just-nonsolvable torsion-free group defined on the binary tree, J. Algebra 211(1999), 99-144.
6. J.W. CANNON, W.I. FLOYD, W.R. PARRY, Introductory notes on Richard Thompson groups, Enseign. Math. (2) 42(1996), 215-256.
7. A. CONNES, Noncommutative Geometry, Academic Press, San Diego 1994.
8. A. CONNES, V. JONES, Property T for von Neumann algebras, Bull. London Math. Soc. 17(1985), 57-62.
9. J. CUNTZ, Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173-185.
10. J. CUNTZ, W. KRIEGER, A class of C*-algebras and topological Markov chains, Invent. Math. 56(1980), 251-268.
11. K.R. DAVIDSON, C*-Algebras by Example, Amer. Math. Soc., Providence, RI, 1996.
12. R.I. GRIGORCHUK, On Burnside's problem on periodic groups, Functional Anal. Appl. 14(1980), 41-43.
13. R.I. GRIGORCHUK, Milnor's problem on the growth of groups. Soviet Math. Dokl. 28(1983), 23-26.
14. R.I. GRIGORCHUK, Degrees of growth of finitely generated groups and the theory of invariant means, Math. USSR Izv. 25(1985), 259-300.
15. R.I. GRIGORCHUK; Just infinite branch groups, in New Horizons in pro-p Groups, Progr. Math., vol. 184, Birkhäuser Boston, Boston 2000, pp. 121-179.
16. R.I. GRIGORCHUK, V.V. NEKRASHEVICH, V.I. SUSHCHANSKII, Automata, dynamical systems and groups, Proc. Steklov Inst. Math. 231(2000), 128-203.
17. R.I. GRIGORCHUK, A. ŻUK, The lamplighter group as a group generated by a 2-state automaton and its spectrum, Geom. Dedicata 87(2001), 209-244.
18. N.D. GUPTA, S.N. SIDKI, On the Burnside problem for periodic groups, Math. Z. 182(1983), 385-388.
19. P. DE LA HARPE, Topics in Geometric Group Theory, University of Chicago Press, Chicago 2000.
20. G. HIGMAN, Finitely Presented Infinite Simple Groups, Notes Pure Math., vol. 8, Department of Pure Mathematics, Department of Mathematics, I.A.S. Australian National University, Canberra, 1974.
21. V. JONES, V.S. SUNDER, Introduction to Subfactors, London Math. Soc. Lecture Note Ser., vol. 234, Cambridge Univ. Press, Cambridge 1997.
22. T. KAJIWARA, C. PINZARI, Y. WATATANI, Ideal structure and simplicity of the C*-algebras generated by Hilbert bimodules, J. Funct. Anal. 159(1998), 295-322.
23. R. MCKENZIE, R.J. THOMPSON, An elementary construction of unsolvable word problems in group theory, in Word Problems: Decision Problems and the Burnside Problem in Group Theory (Conference Univ. California, Irvine, Calif. 1969; dedicated to Hanna Neumann), Stud. Logic Found. Math., vol. 71, North-Holland Publ. Company, Amsterdam, 1973, pp. 457-478.
24. P.S. MUHLY, B. SOLEL, On the simplicity of some Cuntz-Pimsner algebras, Math. Scand. 83(1998), 53-73.
25. V.V. NEKRASHEVYCH, S.N. SIDKI, Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms, in Groups: Topological, Combinatorial and Arithmetic Aspects, London Math. Soc. Lecture Note Ser., vol. 311, Cambridge Univ. Press, Cambridge 2004, pp. 375-404.
26. M.V. PIMSNER, A class of C*-algebras generalizing both Cuntz-Krieger algebras and crossed products by Zℤ, in Free Probability Theory (Waterloo, ON, 1995), Amer. Math. Soc., Providence, RI, 1997, pp. 189-212.
27. C.E. RÖVER, Constructing finitely presented simple groups that contain Grigorchuk groups, J. Algebra 220(1999), 284-313.
28. C.E. RÖVER, Commensurators of groups acting on rooted trees, Geom. Dedicata 94(2002), 45-61.
29. J. SCHWEIZER, Dilations of C*-correspondences and the simplicity of Cuntz-Pimsner algebras, J. Funct. Anal. 180(2001), 404-425.
30. R.J. THOMPSON, Embeddings into finitely generated simple groups which preserve the word problem, in Word Problems. II (Conference on Decision Problems in Algebra, Oxford, 1976), Stud. Logic Found. Math., vol. 95, North-Holand Publ. Company, Amsterdam 1980, pp. 401-441.
31. A. VINCE, Rep-tiling Euclidean space, Aequationes Math. 50(1995), 191-213.
32. A. VINCE, Digit tiling of Euclidean space, in Directions in Mathematical Quasicrystals, Amer. Math. Soc., Providence, RI, 2000, pp. 329-370.