Abstract
Generalizing a result of Furstenberg, we show that, for every infinite discrete group G, the Bernoulli flow is disjoint from every minimal G-flow. From this, we deduce that the algebra generated by the minimal functions is a proper subalgebra of and that the enveloping semigroup of the universal minimal flow is a proper quotient of the universal enveloping semigroup . 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
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