15 March 2021 Bernoulli disjointness
Eli Glasner, Todor Tsankov, Benjamin Weiss, Andy Zucker
Author Affiliations +
Duke Math. J. 170(4): 615-651 (15 March 2021). DOI: 10.1215/00127094-2020-0093

Abstract

Generalizing a result of Furstenberg, we show that, for every infinite discrete group G, the Bernoulli flow 2G is disjoint from every minimal G-flow. From this, we deduce that the algebra generated by the minimal functions A(G) is a proper subalgebra of (G) and that the enveloping semigroup of the universal minimal flow M(G) is a proper quotient of the universal enveloping semigroup βG. When G is countable, we also prove that, for any metrizable, minimal G-flow, there exists a free, minimal flow disjoint from it and that there exist continuum many mutually disjoint minimal, free, metrizable G-flows. Finally, improving a result of Frisch, Tamuz, and Vahidi Ferdowsi and answering a question of theirs, we show that if G is a countable group with infinite conjugacy classes, then it admits a free, minimal, proximal flow.

Citation

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Eli Glasner. Todor Tsankov. Benjamin Weiss. Andy Zucker. "Bernoulli disjointness." Duke Math. J. 170 (4) 615 - 651, 15 March 2021. https://doi.org/10.1215/00127094-2020-0093

Information

Received: 10 October 2019; Revised: 10 July 2020; Published: 15 March 2021
First available in Project Euclid: 1 March 2021

Digital Object Identifier: 10.1215/00127094-2020-0093

Subjects:
Primary: ‎37B05‎
Secondary: 37B10 , 54H20‎

Keywords: Bernoulli flow , disjointness , minimal flows , proximal flows , strongly irreducible subshifts

Rights: Copyright © 2021 Duke University Press

Vol.170 • No. 4 • 15 March 2021
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