C-Tensor Categories and Subfactors for Totally Disconnected Groups

Conference paper
Part of the Abel Symposia book series (ABEL, volume 12)


We associate a rigid C-tensor category \(\mathcal{C}\) to a totally disconnected locally compact group G and a compact open subgroup K < G. We characterize when \(\mathcal{C}\) has the Haagerup property or property (T), and when \(\mathcal{C}\) is weakly amenable. When G is compactly generated, we prove that \(\mathcal{C}\) 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 \(\mathcal{C}\) as the category of bimodules generated by a hyperfinite subfactor.



Y.A. was supported by the Research Fellow of the Japan Society for the Promotion of Science and the Program for Leading Graduate Schools, MEXT, Japan.

S.V. was supported in part by European Research Council Consolidator Grant 614195, and by long term structural funding—Methusalem grant of the Flemish Government.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Graduate School of MathematicsUniversity of TokyoTokyoJapan
  2. 2.Department of MathematicsKU LeuvenLeuvenBelgium

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