发表机构
University of Waterloo; The Ohio State University（滑铁卢大学; 俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入C*-代数包含关系的Property (SP)，研究其性质与持久性，否定解决Furstenburg边界导出的包含关系的相关问题。
AI 中文摘要
作为实秩零C*-代数包含关系的Gabe和Neagu工作的推广，本文引入了C*-代数包含关系的Property (SP)概念，系统开展SP-包含关系研究，建立交换情形下的拓扑刻画及多种构造下的持久性；还将经典对称性下C*-代数Property (SP)的持久性结果推广到量子对称性情形，证明单可分C*-代数的Property (SP)在不可约C*-离散包含关系下保持；最终否定解决了Gabe和Neagu提出的关于Furstenburg边界导出的包含关系的问题，即存在可数离散非 amenable 群G，使得C_r^*(G)⊆C(∂_F G)⋊_r G不是SP-包含关系，因此也不是实秩零的包含关系。
英文摘要
As a generalization of Gabe and Neagu's inclusions of real rank zero, we introduce a notion of Property (SP) for inclusions of C*-algebras. We begin the systematic study of SP-inclusions, establishing a topological description in the commutative setting and permanence under many constructions. We also extend known results about the permanence of Property (SP) for C*-algebras under classical symmetries to the setting of quantum symmetries; we show that Property (SP) for (simple, separable) C*-algebras is preserved under irreducible C*-discrete inclusions. Finally, we resolve (in the negative) a question raised by Gabe and Neagu about inclusions coming from Furstenburg boundaries. Namely, we show the existence of a countable, discrete, non-amenable group $G$ such that $C_r^*(G) \subseteq C(\partial_F G) \rtimes_r G$ is not an SP-inclusion (and therefore not an inclusion of real rank zero).
Comments34 pages + references. Comments welcome!
