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Geometric & Functional Analysis GAFA

, Volume 12, Issue 5, pp 964–988 | Cite as

Minimal actions of the group \( {\Bbb S(Z)} \) of permutations of the integers

  • E. Glasner
  • B. Weiss

Abstract.

Each topological group G admits a unique universal minimal dynamical system (M(G),G). For a locally compact non-compact group this is a nonmetrizable system with a very rich structure, on which G acts effectively. However there are topological groups for which M(G) is the trivial one point system (extremely amenable groups), as well as topological groups G for which M(G) is a metrizable space and for which one has an explicit description. One such group is the topological group \( \Bbb S \) of all the permutations of the integers \( \Bbb Z \), with the topology of pointwise convergence. In this paper we show that (M(\( \Bbb S \)), \( \Bbb S \)) is a symbolic dynamical system (hence in particular M(\( \Bbb S \)) is a Cantor set), and we give a full description of all its symbolic factors.

Keywords

Dynamical System Topological Group Full Description Point System Explicit Description 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • E. Glasner
    • 1
  • B. Weiss
    • 2
  1. 1.Department of Mathematics, Tel Aviv University, Tel Aviv, Israel, e-mail: glasner@math.tau.ac.ilIL
  2. 2.Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel, e-mail: weiss@math.huji.ac.ilIL

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