无自性的非核交叉积
Selfless nonnuclear crossed products
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中文总结 AI 辅助
本文证明了Cantor作用类$\mathrm{A}^*(F_d,X)$的约化交叉积C*-代数的C*-无自性，并推出其具有稳定秩一、严格比较、唯一拟迹态和实秩零等性质。
中文摘要 AI 辅助
我们证明了属于Bell、Geffen和Kerr引入的类$\mathrm{A}^*(F_d,X)$的Cantor作用的约化交叉积C*-代数的C*-无自性。我们由此推出它们具有稳定秩一、严格比较、唯一拟迹态和实秩零。
英文摘要
For a strictly ergodic action of a countable discrete group with Ozawa's property PHP on the Cantor set, we prove that dynamical comparison implies complete selflessness of its reduced crossed product. Therefore these crossed products have stable rank one, strict comparison, a unique quasitracial state, and real rank zero. Applications include probability-measure-preserving Cantor actions of C*-simple acylindrically hyperbolic and C*-simple linear groups for which an infinite amenable subgroup acts strictly ergodically. The results also apply to subodometers and infinite regular Toeplitz subshifts of residually finite groups with PHP.
发表机构
- University of Münster（明斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
