Non-inner amenability of the Thompson groups T and V

In this paper we prove that the Thompson groups T and V are not inner amenable. In particular, their group von Neumann algebras do not have property Γ. Moreover, we prove that if the reduced group C⁎-algebra of T is simple, then the Thompson group F is non-amenable. Furthermore, we give a few new eq...

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Bibliographic Details
Published in:Journal of functional analysis 2017-06, Vol.272 (11), p.4838-4852
Main Authors: Haagerup, Uffe, Olesen, Kristian Knudsen
Format: Article
Language:English
Subjects:
[formula omitted]-simplicity
Amenability
Inner amenability
Thompson groups
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Summary:In this paper we prove that the Thompson groups T and V are not inner amenable. In particular, their group von Neumann algebras do not have property Γ. Moreover, we prove that if the reduced group C⁎-algebra of T is simple, then the Thompson group F is non-amenable. Furthermore, we give a few new equivalent characterizations of amenability of F.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2017.02.003