Journal of Operator Theory

Volume 53, Issue 1, Winter 2005 pp. 185-195.

On the Thompson group factor

Authors: Jaeseong Heo
Author institution: Department of Mathematics, Chungnam National \break University, Taejon 305-764, Korea

Summary: In this article, we will study the structure of the von Neumann algebra

$W^*(F,P)$ generated by the Thompson group von Neumann algebra

$L(F)$ and a projection

$P$ on

$l^2(F)$ . We show that the algebra (not necessarily

$*$ ) algebraically generated by two generating unitaries of the Thompson group factor

$L(F)$ and the commutant

$L(F)'$ is strong-operator dense in

$\BH$ and that

$L_{x_0}^*$ is contained in the strong-operator closure of the algebra (not

$*$ ) generated by

$L_{x_0}$ and the commutant

$L(F)'$ where

$x_0$ is one of generators in

$F$ .

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