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arXiv · 1208.5505

Rigid C^*-tensor categories of bimodules over interpolated free group factors

Arnaud Brothier·Michael Hartglass·David Penneys
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Abstract

Given a countably generated rigid C^*-tensor category C, we construct a planar algebra P whose category of projections Pro is equivalent to C. From P, we use methods of Guionnet-Jones-Shlyakhtenko-Walker to construct a rigid C^*-tensor category Bim whose objects are bifinite bimodules over an interpolated free group factor, and we show Bim is equivalent to Pro. We use these constructions to show C is equivalent to a category of bifinite bimodules over L(F_infty).

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Arnaud Brothier, Michael Hartglass, David Penneys. 2012-08-27. Rigid C^*-tensor categories of bimodules over interpolated free group factors. https://doi.org/10.1063/1.4769178

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