Lifting shadings on symmetrically self-dual subfactor planar algebras

Published 15 Sep 2017 in math.OA, math.CT, and math.QA | (1709.05023v1)

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.

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