The Inner Amenability of the Generalized Thompson Group

Details The Inner Amenability of the Generalized Thompson Group The Inner Amenability of the Generalized Thompson Group

2004-04-30

arxiv.org/abs/math/0404552v3

Mathematics

Operator Algebras

A "Background" section has been added; to appear in Proceedings of the AMS

Scientific paper

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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