Invariant random subgroups and action versus representation maximality
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- by Peter J. Burton and Alexander S. Kechris PDF
- Proc. Amer. Math. Soc. 145 (2017), 3961-3971 Request permission
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.References
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Additional Information
- Peter J. Burton
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 984415
- Email: pjburton@caltech.edu
- Alexander S. Kechris
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 99660
- Email: kechris@caltech.edu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3961-3971
- MSC (2010): Primary 28D15, 37A35
- DOI: https://doi.org/10.1090/proc/13591
- MathSciNet review: 3665047