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arXiv · 1602.03047

C*-tensor categories and subfactors for totally disconnected groups

Yuki Arano·Stefaan Vaes
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Abstract

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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Yuki Arano, Stefaan Vaes. 2016-02-09. C*-tensor categories and subfactors for totally disconnected groups. https://doi.org/10.1007/978-3-319-39286-8_1

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