Planar algebras: a category theoretic point of view

Details Planar algebras: a category theoretic point of view Planar algebras: a category theoretic point of view

2008-10-23

arxiv.org/abs/0810.4186v3

Mathematics

Quantum Algebra

24 pages, Version 2, some minor changes and typographical errors corrected in sections 2.2 and 4

Scientific paper

We define Jones's planar algebra as a map of multicategories and constuct a planar algebra starting from a 1-cell in a pivotal strict 2-category. We prove finiteness results for the affine representations of finite depth planar algebras. We also show that the radius of convergence of the dimension of an affine representation of the planar algebra associated to a finite depth subfactor is at least as big as the inverse-square of the modulus.

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