非核Bunce-Deddens代数
Nonnuclear Bunce-Deddens algebras
浏览论文内容
中文总结 AI 辅助
本文引入非核Bunce-Deddens代数，证明其具有多种正则性质，还计算了非阿贝尔自由群上该类代数的K-理论。
中文摘要 AI 辅助
我们引入非核Bunce-Deddens代数，将其定义为非可分可数离散残余有限群的自由odometer作用在Cantor空间上的约化交叉积C*-代数，它们是Orfanos引入的广义Bunce-Deddens代数的非核对应物。对于大类群，我们证明其具有实秩零、稳定秩一、正元严格比较、唯一迹态等正则性质；多数情况下还满足自反性（selfless），故为纯代数。最后，我们计算了非阿贝尔自由群上Bunce-Deddens代数的K-理论。
英文摘要
We introduce nonnuclear Bunce-Deddens algebras, defined as reduced crossed product C*-algebras associated with free odometer actions of nonamenable countable discrete residually finite groups on a Cantor space. These are nonnuclear counterparts to the generalised Bunce-Deddens algebras introduced by Orfanos. For large classes of groups, we show that they share many regularity properties, including real rank zero, stable rank one, strict comparison of positive elements, and admitting a unique tracial state. In many cases, we deduce that they are even selfless and hence pure. Finally, we compute the K-theory of Bunce-Deddens algebras over nonabelian free groups.
