AI 中文总结
该研究针对离散群作用于紧空间的稳定子相关C*-代数，利用Rieffel诱导方法，证明当空间为极端边界时，对应群C*-代数纯无限，回答了汤普森群相关C*-代数的部分问题
AI 中文摘要
给定一个作用在紧空间$X$上的离散群$\text{Γ}$，以及$X$的一个稳定子子群$\text{Λ} \text{≤} \text{Γ}$，我们利用共变$(\text{Λ}, X)$表示的Rieffel诱导，研究由$\text{Λ}$上的某些特征标及其生成的$\text{C}^*$-代数所诱导的表示类。当$X$是一个$\text{Γ}$-边界时，我们得到了新一类单的、无迹的群$\text{C}^*$-代数。当$\text{Γ}$-边界$X$是极端边界时，我们证明对应的群$\text{C}^*$-代数也是纯无限的，回答了Kalantar和Scarparo关于与汤普森群相关的$\text{C}^*$-代数提出的问题的一部分。这类$\text{C}^*$-代数还被证明具有Robert意义下的无私性。
英文摘要
Given a discrete group $Γ$ acting on a compact space $X$, and a stabilizer subgroup $Λ\leq Γ$ of $X$, we use the Rieffel induction of covariant $(Λ, X)$-representations to study classes of representations induced by certain characters on $Λ$ and the $\text{C}^*$-algebras they generate. When $X$ is a $Γ$-boundary, we obtain new classes of simple, traceless group $\text{C}^*$-algebras. When the $Γ$-boundary $X$ is an extreme boundary, we show that the associated group $\text{C}^*$-algebras are also purely infinite, answering part of a question posed by Kalantar and Scarparo on $\text{C}^*$-algebras associated with Thompson's groups. The latter $\text{C}^*$-algebras are shown to be selfless in the sense of Robert.
Comments14 pages. Comments welcome!
