On universal minimal proximal flows of topological groups

2017/08/08 by Xiongping Dai, Eli Glasner, Dai, Xiongping +1
Mathematics · #37B05 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1708.02468

openalex publication_date 2017/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ([Theorem~II.4.4]) 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 Comm_G(H).

Related

• Universal minimal flows of extensions of and by compact groups
• Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
• On minimal flows. definably amenable groups, and o-minimality
• Minimal model-universal flows for locally compact Polish groups
• A direct solution to the Generic Point Problem