Lifting shadings on symmetrically self-dual subfactor planar algebras

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.

在本文中，我们讨论了阴影平面代数的对称自对偶性这一概念，它使我们能够提升子因子平面代数上的阴影，从而得到\(\mathbb{Z}/2\mathbb{Z}\) - 分次酉融合范畴。这完成了存在融合图为\(4442\)和\(3333\)的酉融合范畴的证明。