J. Aust. Math. Soc.  79 (2005), 231-241
Operator algebras related to Thompson's group F

Paul Jolissaint
  Institut de Mathémathiques
  Université de Neuch\^atel
  Emile-Argand 11
  CH-2000 Neuch\^atel
  Switzerland
  paul.jolissaint@unine.ch


Abstract
Let $F'$ be the commutator subgroup of $F$ and let $\Gamma_0$ be the cyclic group generated by the first generator of $F$. We continue the study of the central sequences of the factor $L(F')$, and we prove that the abelian von Neumann algebra $L(\Gamma_0)$ is a strongly singular MASA in $L(F)$. We also prove that the natural action of $F$ on $[0,1]$ is ergodic and that its ratio set is $\{0\}\cup\{2^k; k\in\mathbb Z\}$.
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