Uniformly recurrent subgroups and the ideal structure of reduced crossed products Article Swipe

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Takuya Kawabe ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1701.03413 · OA: W2590008704

We study the ideal structure of reduced crossed product of topological dynamical systems of a countable discrete group. More concretely, for a compact Hausdorff space $X$ with an action of a countable discrete group $Γ$, we consider the absence of a non-zero ideals in the reduced crossed product $C(X) \rtimes_r Γ$ which has a zero intersection with $C(X)$. We characterize this condition by a property for amenable subgroups of the stabilizer subgroups of $X$ in terms of the Chabauty space of $Γ$. This generalizes Kennedy's algebraic characterization of the simplicity for a reduced group $\mathrm{C}^{*}$-algebra of a countable discrete group.