全不连通的群的C*-张量范畴和子因子
C*-tensor categories and subfactors for totally disconnected groups
摘要：
我们将刚性C*-张量范畴$C$与一个全不连通的局部紧群$G$和一个紧开子群$K < G$联系起来.我们刻画了$C$何时具有Haagerup性质或性质（T），以及何时$C$是弱顺从的.当$G$是紧生成的时，我们证明了$C$本质上等价于Jones和Burstein将平面代数与作用在局部有限二部图上的群相联系.然后，我们具体实现$C$作为范畴的双模产生的超有限子因子。
英文摘要：
We associate a rigid C*-tensor category $C$ to a totally disconnected locally compact group $G$ and a compact open subgroup $K < G$. We characterize when $C$ has the Haagerup property or property (T), and when $C$ is weakly amenable. When $G$ is compactly generated, we prove that $C$ is essentially equivalent to the planar algebra associated by Jones and Burstein to a group acting on a locally finite bipartite graph. We then concretely realize $C$ as the category of bimodules generated by a hyperfinite subfactor.
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