On universal minimal proximal flows of topological groups
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- by Xiongping Dai and Eli Glasner PDF
- Proc. Amer. Math. Soc. 147 (2019), 1149-1164 Request permission
Abstract:
In this paper, we show that the action of a characteristically simple, non-extremely amenable (non-strongly amenable, non-amenable) group on its universal minimal (minimal proximal, minimal strongly proximal) flow is effective. We present necessary and sufficient conditions, for the action of a topological group with trivial center on its universal minimal proximal flow, to be effective. A theorem of Furstenberg about the isomorphism of the universal minimal proximal flows of a discrete group and its subgroups of finite index ([Proximal flows, Springer-Verlag, Berlin-New York, 1976]) is strengthened. Finally, for a pair of groups $H < G$ the same method is applied in order to extend the action of $H$ on its universal minimal proximal flow to an action of its commensurator group $\mathrm {Comm}_G(H)$.References
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Additional Information
- Xiongping Dai
- Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
- MR Author ID: 609395
- Email: xpdai@nju.edu.cn
- Eli Glasner
- Affiliation: Department of Mathematics, Tel Aviv University, Tel Aviv, Israel
- MR Author ID: 271825
- ORCID: 0000-0003-1167-1283
- Email: glasner@math.tau.il
- Received by editor(s): February 5, 2018
- Received by editor(s) in revised form: April 29, 2018, June 9, 2018, and June 13, 2018
- Published electronically: November 16, 2018
- Additional Notes: The first author was partly supported by National Natural Science Foundation of China (Grant Nos. 11431012, 11790274)
The second author was supported by a grant of the Israel Science Foundation (ISF 668/13). - Communicated by: Nimish Shah
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1149-1164
- MSC (2010): Primary 37B05
- DOI: https://doi.org/10.1090/proc/14292
- MathSciNet review: 3896063