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arXiv · 2404.13436

Faithful actions on generalized Furstenberg boundary

Farid Behrouzi·Zahra Naghavi
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Abstract

Let $G$ be a countable discrete group that act 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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Farid Behrouzi, Zahra Naghavi. 2024-04-20. Faithful actions on generalized Furstenberg boundary. https://arxiv.org/abs/2404.13436

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