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

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).

50 pages, many figures

References in corpus (2)

• Random matrices, free probability, planar algebras and subfactors
• Representations of multicategories of planar diagrams and tensor categories

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