Abstract
Let \( {\mathcal{G}} \) be a locally compact groupoid. We show that there is a one-to-one correspondence between \( {\mathcal{G}} \)-spaces and the groupoid dynamical systems whose underling \( C_{0}({{\mathcal{G}}}^{(0)}) \)-algebra is commutative. We study minimality and (strong) proximality for \( {\mathcal{G}} \)-actions and show that each locally compact groupoid \( {\mathcal{G}} \) has a universal minimal (strongly) proximal \( {\mathcal{G}} \)-space (called the Furstenberg boundary).
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Funding
The first author was partially supported by a grant from the IPM (Project 96460118).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 5, pp. 953–964. https://doi.org/10.33048/smzh.2021.62.501
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M., A., F., B. The Furstenberg Boundary of Groupoids. Sib Math J 62, 773–781 (2021). https://doi.org/10.1134/S0037446621050013
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DOI: https://doi.org/10.1134/S0037446621050013