Operator algebras related to Thompson's group F

Jolissaint, Paul

In: Journal of the Australian Mathematical Society, 2005, vol. 79, no. 2, p. 231-241

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    Let F′ be the commutator subgroup of F and let Γ0 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(Γ0) 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} {2k; k ∞ Z}