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The inner amenability of the generalized Thompson group
Author:
Gabriel Picioroaga
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1995-2002
MSC (2000):
Primary 46K10, 22D15
Posted:
December 19, 2005
MathSciNet review:
2215768
Full-text PDF Free Access
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Abstract: In this paper we prove that the general version  of the Thompson group is inner amenable. As a consequence we generalize a result of P. Jolissaint. To do so, we prove first that  together with a normal subgroup are i.c.c (infinite conjugacy classes) groups. Then, we investigate the relative McDuff property out of which we extract property  for the group von Neumann algebras involved. By a result of E. G. Effros,  follows inner amenable.
References
- [Br]
K.S. Brown, Finiteness Properties of Groups, J. Pure Appl. Algebra, 44 (1986), 45-75. MR 0885095 (88m:20110)
- [Can]
J.W. Cannon, W.J. Floyd, and W.R. Parry, Introductory Notes on Richard Thompson's Groups, L'Enseignement Mathematique, 42 (1996), pp. 215-256. MR 1426438 (98g:20058)
- [Che]
T.G. Ceccherini-Silberstein, Around Amenability, Journal of Mathematical Sciences, Vol. 106, No. 4, 2001. MR 1871137 (2003d:43003)
- [vDa]
A. van Daele, Crossed Products of von Neumann Algebras, Lecture Notes Series, London Math. Soc., 1978.
- [DutP]
D. Dutkay, G. Picioroaga, The von Neumann Algebra of the Canonical Equivalence Relation of the Thompson Group , 2004, arxiv id math.OA/0403332.
- [Efr]
E.G. Effros, Property
 and Inner Amenability, Proc. Amer. Math. Soc., 47 (1975), 483-486. MR 0355626 (50:8100)
- [Hig]
G. Higman, Finitely Presented Infinite Simple Groups, Notes on Pure Math., vol. 8, Australian National University, Canberra, 1974. MR 0376874 (51:13049)
- [Jol1]
P. Jolissaint, Moyennabilite Interieure du Groupe F de Thompson, C.R. Acad. Sci. Paris, Serie I, 325 (1997), 61-64. MR 1461398 (98j:20049)
- [Jol]
P. Jolissaint, Central Sequences in the Factor Associated with the Thompson's Group F, Annales de l'institut Fourier, tome 48, no. 4 (1998), pp. 1093-1106. MR 1656009 (2000b:46108)
- [St]
M. Stein, Groups of Piecewise Linear Homeomorphisms, Trans. Amer. Math. Soc., 332 (1992), no. 2, 477-514. MR 1094555 (92k:20075)
- [StZ]
S. Stratila, L. Zsido, Lectures on von Neumann Algebras, Bucuresti, Romania, Editura Academiei; Tunbridge Well, Kent, England, Abacus Press, 1979. MR 0526399 (81j:46089)
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Additional Information
Gabriel Picioroaga
Affiliation:
Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419
Address at time of publication:
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230, Odense M, Denmark
Email:
gpicioro@math.uiowa.edu, gpicioro@imada.sdu.dk
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08236-5
PII:
S 0002-9939(05)08236-5
Received by editor(s):
February 8, 2005
Posted:
December 19, 2005
Communicated by:
David R. Larson
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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