On universal minimal proximal flows of topological groups

Xiongping Dai, Eli Glasner

Research output: Contribution to journalArticlepeer-review

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 CommG(H).

Original languageEnglish
Pages (from-to)1149-1164
Number of pages16
JournalProceedings of the American Mathematical Society
Volume147
Issue number3
DOIs
StatePublished - Mar 2019

Funding

FundersFunder number
National Natural Science Foundation of China11431012, 11790274
Israel Science FoundationISF 668/13

    Keywords

    • Effective action
    • Strong/extreme amenability
    • Universal minimal proximal flow

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