Furstenberg boundary of minimal actions
Operator Algebras
2019-06-04 v2
Abstract
For a countable discrete group {\Gamma} and a minimal {\Gamma}-space X, we study the notion of ({\Gamma}, X)-boundary, which is a natural generalization of the notion of topological {\Gamma}-boundary in the sense of Furstenberg. We give characterizations of the ({\Gamma}, X)-boundary in terms of essential or proximal extensions. The characterization is used to answer a problem of Hadwin and Paulsen in negative. As an application, we find necessary and sufficient condition for the corresponding reduced crossed product to be exact.
Cite
@article{arxiv.1905.01841,
title = {Furstenberg boundary of minimal actions},
author = {Zahra Naghavi},
journal= {arXiv preprint arXiv:1905.01841},
year = {2019}
}