Non-inner amenability of the Thompson groups T and V

Uffe Haagerup; Kristian Knudsen Olesen

Non-inner amenability of the Thompson groups T and V

Operator Algebras 2016-09-19 v1 Group Theory

Authors: Uffe Haagerup , Kristian Knudsen Olesen

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 $\Gamma$ . Moreover, we prove that if the reduced group $C^\ast$ -algebra of $T$ is simple, then the Thompson group $F$ is non-amenable. Furthermore, we give a few new equivalent characterizations of amenability of $F$ .

Keywords

Thompson groups inner amenable von Neumann algebras property Gamma reduced group C*-algebra amenable

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@article{arxiv.1609.05086,
  title  = {Non-inner amenability of the Thompson groups T and V},
  author = {Uffe Haagerup and Kristian Knudsen Olesen},
  journal= {arXiv preprint arXiv:1609.05086},
  year   = {2016}
}

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13 pages

Non-inner amenability of the Thompson groups T and V

Abstract

Keywords

Cite

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