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Invariant random subgroups and action versus representation maximality


Authors: Peter J. Burton and Alexander S. Kechris
Journal: Proc. Amer. Math. Soc. 145 (2017), 3961-3971
MSC (2010): Primary 28D15, 37A35
DOI: https://doi.org/10.1090/proc/13591
Published electronically: April 7, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that weak containment of free ergodic measure-
preserving actions of $ \mathbb{F}_\infty $ is not equivalent to weak containment of the corresponding Koopman representations. This result is based on the construction of an invariant random subgroup of $ \mathbb{F}_\infty $ which is supported on the maximal actions.


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Additional Information

Peter J. Burton
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: pjburton@caltech.edu

Alexander S. Kechris
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: kechris@caltech.edu

DOI: https://doi.org/10.1090/proc/13591
Received by editor(s): August 25, 2016
Received by editor(s) in revised form: October 12, 2016
Published electronically: April 7, 2017
Additional Notes: Research partially supported by NSF Grant DMS-1464475
Communicated by: Adrian Ioana
Article copyright: © Copyright 2017 American Mathematical Society