Gromov's translation algebras, growth and amenability of operator algebras

Expositiones Mathematicae

Volumn 26, Issue 2, 2008, Pages 141-162

  Ceccherini Silberstein, T G ^a   Samet Vaillant, A Y ^b  

^a UNIVERSITY OF SANNIO   (Italy)

^b Avinoam Yellin 16   (Israel)

Author keywords

algebras; Amenability; C^{*< sup> algebras; Finitely generated; F lner condition; F lner sequence; Translation algebras}

Indexed keywords

EID: 41549123677     PISSN: 07230869     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.exmath.2007.09.001     Document Type: Article

References (40)

1. Ara P., O'Meara K.C., and Perera F. Gromov translation algebras over discrete trees are exchange rings. Trans. Amer. Math. Soc. 356 (2004) 2067-2079
2. Arveson W. Improper filtrations for C*-algebras: spectra of unilateral tridiagonal operators. Acta Sci. Math. (Szeged) 57 (1993) 11-24
3. L. Bartholdi, On amenability of group algebras, Israel J. Math. (to appear).
4. Bédos E. On filtrations for C*-algebras. Houston J. Math. 20 (1994) 63-74
5. Bédos E. Notes on hypertraces and C*-algebras. J. Operator Theory 34 (1995) 285-306
6. Berele A. Homogeneous polynomial identities. Israel J. Math. 42 (1982) 258-272
7. B. Blackadar, The algebraization of dynamics: amenability, nuclearity, quasidiagonality, and approximate finite dimensionality, in: Operator algebras, quantization, and noncommutative geometry, 51-83, Contemp. Math., 365, Amer. Math. Soc., Providence, RI, 2004.
8. Block J., and Weinberger S. Aperiodic tilings, positive scalar curvature, and amenability of spaces. J. Amer. Math. Soc. 5 (1992) 907-918
9. J. Block, S. Weinberger, Large scale homology theories and geometry, in: Geometric topology (Athens, GA, 1993), 522-569, AMS/IP Stud. Adv. Math., 2.1, Amer. Math. Soc., Providence, RI, 1997.
10. Ceccherini-Silberstein T.G., Grigorchuk R.I., and de la Harpe P. Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces. Proc. Steklov Inst. Math. 224 (1999) 57-97
11. Connes A. Classification of injective factors. Ann. Math. 104 (1976) 73-115
12. Connes A. Compact metric spaces, Fredholm modules and hyperfiniteness. Ergodic Theory and Dynamical Systems 9 (1989) 207-220
13. Connes A. Noncommutative Geometry (1994), Academic Press, San Diego, CA
14. K.R. Davidson, C*-algebras by example, Fields Institute Monographs, 6. American Mathematical Society, Providence, RI, 1996.
15. Elek G. The K-theory of Gromov's translation algebras and the amenability of discrete groups. Proc. Amer. Math. Soc. 125 (1997) 2551-2553
16. G. Elek, The Hochschild cohomologies of translation algebras and group cohomologies, see 〈http://www.math.uiuc.edu/K-theory/0190/〉, preprint of the Mathematical Institute of the Hungarian Academy of Science, 1997.
17. Elek G. The amenability of affine algebras. J. Algebra 264 (2003) 469-478
18. Følner E. On groups with full Banach mean value. Math. Scand. 3 (1955) 243-254
19. F. Greenleaf, Mean invariant on topological groups, Van Nostrand, 1969.
20. R. Grigorchuk, P. Kurchanov, Some questions of group theory related to geometry, Encycl. of Math. Sciences, vol. 58, Algebra VII, Springer, Berlin, 1993.
21. M. Gromov, Asymptotic invariants of infinite groups, in: Graham A. Niblo, Martin A. Roller (Eds.), Geometric group theory, vol. 2 (Sussex, 1991), pp. 1-295, London Mathematical Society Lecture Note Series 182, Cambridge University Press, Cambridge, UK, 1993.
22. P. de la Harpe, Operator algebras free groups and other groups, in: Recent advances in operator algebras (Orléans, 1992), Astérisque 232 (1995) 121-153.
23. A.Ya. Helemskii, The homology of Banach and topological algebras, Translated from the Russian by Alan West. Mathematics and its Applications (Soviet Series), 41. Kluwer Academic Publishers Group, Dordrecht, 1989.
24. Kaimanovich V.A., and Vershik A.M. Random walks on discrete groups: boundary and entropy. Annals Prob. 11 (1983) 457-490
25. Kirchberg E., and Vaillant G. On C*-algebras having linear, polynomial and subexponential growth. Invent. Math. 108 (1992) 635-652
26. G. Krause, T. Lenagan, Growth of algebras and the Gelfand-Kirillov dimension, Revised edition, Graduate Studies in Mathematics, 22, American Mathematical Society, Providence, RI, 2000.
27. von Neumann J. Zur allgemeinen Theorie des Masses. Fund. Math. 13 (1929) 73-116
28. A.L.T. Paterson, Amenability, Mathematical Surveys and Monographs, vol. 29, American Mathematical Society, Providence, RI, 1988.
29. Pittet C. Følner sequences in Polycyclic Groups. Revista Matematica Ibanoamericana 11 (1995) 675-685
30. C. Pittet, L. Saloff-Coste, Amenable groups, isoperimetric profiles and random walks, in: J. Cossey, C.F. Miller III, W.D. Newmann, M. Shapir (Eds.), Geometric group theory down under, (Camberra, 1996); Walter de Gruyter, 1999, pp. 296-316.
31. Roe J. Finite propagation speed and Connes' foliation algebra. Math. Proc. Cambridge Philos. Soc. 102 (1987) 459-466
32. Roe J. An index theorem on open manifolds I-II. J. Differential Geometry 27 (1988) 87-136
33. J. Roe, Exotic cohomology and index theory on complete Riemannian manifolds, preprint, 1990.
34. Samet-Vaillant A.Y. C*- algebras, Gelfand-Kirillov dimension and Følner sets. J. Funct. Anal. 171 (2000) 346-365
35. Samet-Vaillant A.Y. Free*-subalgebras of C*-algebras. J. Funct. Anal. 171 (2000) 432-448
36. Ufnarovski V. Combinatorial and asymptotic methods in algebra, Encyclopedia of Math. Sciences, Algebra VI vol. 57 (1995), Springer, Berlin
37. Vaillant G. Følner conditions, nuclearity, and subexponential growth in C*-algebras. J. Funct. Anal. 141 (1996) 435-448
38. D. Voiculescu, A note on quasidiagonal operators in: Topics in operator theory, Constantin Apostol Memorial Issue, Operator Theory, Advances and Applications, vol. 32, Birkhäuser, Basel, 1988. pp. 265-274.
39. Voiculescu D. On the existence of quasi-central approximate units relative to normed ideals. J. Funct. Anal. 91 (1990) 1-36
40. Wagon S. The Banach-Tarski paradox [Corrected reprint of the 1985 original] (1993), Cambridge University Press, Cambridge