Lifting shadings on symmetrically self-dual subfactor planar algebras

Abstract

In this note, we discuss the notion of symmetric self-duality of shaded planar algebras, which allows us to lift shadings on subfactor planar algebras to obtain Z/2Z-graded unitary fusion categories. This finishes the proof that there are unitary fusion categories with fusion graphs 4442 and 3333.

References in corpus (2)

• Cyclotomic integers, fusion categories, and subfactors
• The classification of $3^n$ subfactors and related fusion categories

Cited by in corpus (2)

• Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories
• Quon language: surface algebras and Fourier duality