The inner amenability of the generalized Thompson group

Picioroaga, Gabriel

doi:10.1090/S0002-9939-05-08236-5

The inner amenability of the generalized Thompson group
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by Gabriel Picioroaga PDF

Proc. Amer. Math. Soc. 134 (2006), 1995-2002 Request permission

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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