Rigid actions need not be strongly ergodic
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- by Adrian Ioana and Stefaan Vaes PDF
- Proc. Amer. Math. Soc. 140 (2012), 3283-3288 Request permission
Abstract:
A probability measure preserving action $\Gamma \curvearrowright (X,\mu )$ is called rigid if the inclusion of $\mathrm {L}^\infty (X)$ into the crossed product $\mathrm {L}^\infty (X) \rtimes \Gamma$ has the relative property (T) in the sense of Popa. We give examples of rigid, free, probability measure preserving actions that are ergodic but not strongly ergodic. The same examples show that rigid actions may admit non-rigid quotients.References
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Additional Information
- Adrian Ioana
- Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
- Address at time of publication: Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
- Email: adiioana@math.ucla.edu, aioana@math.ucsd.edu
- Stefaan Vaes
- Affiliation: Department of Mathematics, K.Β U. Leuven, Celestijnenlaan 200B, Bβ3001 Leuven, Belgium
- Email: stefaan.vaes@wis.kuleuven.be
- Received by editor(s): September 21, 2010
- Received by editor(s) in revised form: April 4, 2011
- Published electronically: February 3, 2012
- Additional Notes: The first author was supported by a Clay Research Fellowship
The second author was partially supported by ERC Starting Grant VNALG-200749, Research Programme G.0231.07 of the Research Foundation, Flanders (FWO) and K.U. Leuven BOF research grant OT/08/032. - Communicated by: Marius Junge
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3283-3288
- MSC (2010): Primary 28D15, 46L10; Secondary 37A20
- DOI: https://doi.org/10.1090/S0002-9939-2012-11261-4
- MathSciNet review: 2917100