Faithful actions on generalized Furstenberg boundary

Behrouzi, Farid; Naghavi, Zahra

doi:10.1090/proc/16928

Faithful actions on generalized Furstenberg boundary
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by Farid Behrouzi and Zahra Naghavi;

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/16928

Published electronically: June 27, 2025

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Abstract:

Let $G$ be a countable discrete group that acts minimally on a compact Hausdorff space $X$ by homeomorphisms. Our goal is to establish the equivalence between the faithfulness of the action of $G$ on the generalized Furstenberg boundary $\partial _F(G, X)$ and a weakened version of the generalized Powers’ averaging property. This result provides valuable insights into the state space of the crossed product $C(X)\rtimes _{r}G$.

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Faithful actions on generalized Furstenberg boundary
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Abstract: