Singly generated planar algebras of small dimension, Part III

Abstract

The first two authors classified subfactor planar algebra generated by a non-trivial 2-box subject to the condition that the dimension of 3-boxes is at most 12 in Part I; 13 in Part II of this series. They are the group planar algebra for ${\mathbb{Z}}_3$, the Fuss-Catalan planar algebra ; and the group/subgroup planar algebra for ${\mathbb{Z}}_2\subset {\mathbb{Z}}_5⋊{\mathbb{Z}}_2$. In the present paper, we extend the classification to 14 dimensional 3-boxes. They are all BMW. Precisely it contains a depth 3 one from quantum $SO(3)$, and a one-parameter family from quantum $Sp(4)$.

arXiv comment15 pages, 34 figures

References in corpus (6)

• Applications of braided endomorphisms from conformal inclusions
• The classification of subfactors of index at most 5
• Skein theory for the D_{2n} planar algebras
• Subfactors of index less than 5, part 2: triple points
• Subfactors of index less than 5, part 3: quadruple points
• Unitarizablity of premodular categories

Cited by in corpus (2)

• Yang-Baxter relation planar algebras
• Towards a classification of compact quantum groups of Lie type