约化交叉积的单纯性
Simplicity of reduced crossed products
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中文总结 AI 辅助
该研究通过稳定子群刻画了极小G-流对应的约化交叉积C*-代数的单纯性，证明其单纯性等价于X中点的C*-单纯稳定子群条件，并给出不可数群不适用该结果的例子，解决了Ozawa的问题。
中文摘要 AI 辅助
我们通过稳定子群刻画约化交叉积C*-代数的单纯性。具体而言，若G是可数群且X是极小G-流，则约化交叉积C*-代数C(X)×_λ G是单纯的，当且仅当X中存在一个点具有C*-单纯稳定子群；进一步，这些条件等价于X的一个通有点具有C*-单纯稳定子群。我们还提供一个例子，表明该结果无法推广到不可数群，这完全解决了Ozawa的一个问题。
英文摘要
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 $\mathrm{C}(X) \times_λG$ 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.
发表机构
- University of Waterloo（滑铁卢大学）
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