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Operator algebras related to Thompson's group F

Part of: Abstract harmonic analysis Ergodic theory

Published online by Cambridge University Press:  09 April 2009

Paul Jolissaint
Paul Jolissaint
Affiliation:
Institut de Mathémathiques, Université de Neuchâtel, Emile-Argand 11, CH-2000 Neuchâtel, Switzerland, e-mail: paul.jolissiant@unine.ch
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Abstract

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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}.

MSC classification

Secondary: 37A10: One-parameter continuous families of measure-preserving transformations 43A07: Means on groups, semigroups, etc.; amenable groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 2 , October 2005 , pp. 231 - 241
Copyright
Copyright © Australian Mathematical Society 2005

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