Non-inner amenability of the Thompson groups T and V

2016/09/16 by Haagerup, Uffe, Olesen, Kristian Knudsen · 5 citations
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1609.05086

Abstract

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.

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• Frame Vector Group Representations and Amenability Properties
• On Similarity Structure Groups and their W^* and C^*-Algebras

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