Planar algebras: a category theoretic point of view
Quantum Algebra
2010-04-07 v3 Operator Algebras
Abstract
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.
Cite
@article{arxiv.0810.4186,
title = {Planar algebras: a category theoretic point of view},
author = {Shamindra Kumar Ghosh},
journal= {arXiv preprint arXiv:0810.4186},
year = {2010}
}
Comments
24 pages, Version 2, some minor changes and typographical errors corrected in sections 2.2 and 4