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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
Published electronically: December 19, 2005
MathSciNet review: 2215768
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Abstract: In this paper we prove that the general version $ F(N)$ of the Thompson group is inner amenable. As a consequence we generalize a result of P. Jolissaint. To do so, we prove first that $ F(N)$ 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 $ \Gamma$ for the group von Neumann algebras involved. By a result of E. G. Effros, $ F(N)$ follows inner amenable.

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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

Received by editor(s): February 8, 2005
Published electronically: December 19, 2005
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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