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arXiv · 2608.17025

Simplicity of reduced crossed products

Thomas Bray·Matthew Kennedy
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Abstract

We characterize the simplicity of reduced crossed product C*-algebras in terms of stabilizer subgroups. Specifically, we prove that if $G$ is a countable group and $X$ is a minimal $G$-flow, then the reduced crossed product C*-algebra $\mathrm{C}(X) \times_\lambda G$ is simple if and only if there is a point in $X$ with a C*-simple stabilizer subgroup. Further, these conditions are equivalent to a generic point in $X$ having a C*-simple stabilizer subgroup. We also provide an example demonstrating that this result does not extend to uncountable groups. This completely resolves a question of Ozawa.

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Thomas Bray, Matthew Kennedy. 2026-08-17. Simplicity of reduced crossed products. https://arxiv.org/abs/2608.17025

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