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 $F$.

Keywords: Thompson group, normal form, transitive algebra, approximately inner automorphism.

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