Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Special Issue: New Trends in Infinite Dimensional Analysis and Quantum Probability
On the Question of the Thompson Group
Jaeseong HEO
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2009 Volume 15 Issue 3 Pages 339-344

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Abstract

This survey is concerned with the Thompson group F and the von Neumann algebra L(F) associated with F. We first review some basic results on the Thompson groups and group von Neumann algebras. We investigate the structure of the von Neumann algebra W*(F,P) generated by L(F) and a projection P on l2(F). We show that the algebra (not necessarily *) algebraically generated by two generating unitaries of L(F) and the commutant L(F)′ is strong-operator dense in {\\mathcal B}({\\mathcal H}). Furthermore, we will discuss actions of F and F′ on a set of dyadic rational numbers in [0,1] and some outer automorphism of L(F) for the amenability question of F.

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© 2009 by the Graduate School of Information Sciences (GSIS), Tohoku University

This article is licensed under a Creative Commons [Attribution 4.0 International] license.
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