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Minimal flows with arbitrary centralizer

Part of: Topological dynamics Noncompact transformation groups

Published online by Cambridge University Press:  29 December 2020

ANDY ZUCKER Open the ORCID record for ANDY ZUCKER [Opens in a new window]
ANDY ZUCKER*
Affiliation:
Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA92093, USA
*
e-mail:azucker@ucsd.eduu
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Abstract

Given a G-flow X, let $\mathrm{Aut}(G, X)$ , or simply $\mathrm{Aut}(X)$ , denote the group of homeomorphisms of X which commute with the G action. We show that for any pair of countable groups G and H with G infinite, there is a minimal, free, Cantor G-flow X so that H embeds into $\mathrm{Aut}(X)$ . This generalizes results of [2, 7].

Keywords

minimal flowcentralizerblueprintstrongly irreducible shift

MSC classification

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Secondary: 37B10: Symbolic dynamics 22F50: Groups as automorphisms of other structures
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 1 , January 2022 , pp. 310 - 320
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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