A planar calculus for infinite index subfactors

Abstract

We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.

56 pages, many figures

References in corpus (3)

• Random matrices, free probability, planar algebras and subfactors
• Subfactors of index less than 5, part 3: quadruple points
• Subfactors, Planar Algebras and Rotations

Cited by in corpus (8)

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• Rigid C^*-tensor categories of bimodules over interpolated free group factors
• Q-system completion for C* 2-categories
• Drinfeld center of planar algebra
• A Diagrammatic Multivariate Alexander Invariant of Tangles
• Free probability, planar algebras, and the multicolored Guionnet-Jones-Shlyakhtenko construction
• A categorical Connes' $\chi (M)$
• Infinite index subfactors and the GICAR categories