TY - JOUR

T1 - Bernoulli disjointness

AU - Glasner, Eli

AU - Tsankov, Todor

AU - Weiss, Benjamin

AU - Zucker, Andy

N1 - Publisher Copyright:
© 2021

PY - 2021/3/15

Y1 - 2021/3/15

N2 - 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 ℓ∞(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.

AB - 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 ℓ∞(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.

UR - http://www.scopus.com/inward/record.url?scp=85106650951&partnerID=8YFLogxK

U2 - 10.1215/00127094-2020-0093

DO - 10.1215/00127094-2020-0093

M3 - מאמר

AN - SCOPUS:85106650951

VL - 170

SP - 615

EP - 651

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 4

ER -