Lifting shadings on symmetrically self-dual subfactor planar algebras

Zhengwei Liu Scott Morrison David Penneys

Category Theory Quantum Algebra Spectral Theory and Operator Algebra mathscidoc:2207.04002

Contemporary Mathematics, 747, 2020.7
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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@inproceedings{zhengwei2020lifting,
  title={Lifting shadings on symmetrically self-dual subfactor planar algebras},
  author={Zhengwei Liu, Scott Morrison, and David Penneys},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703162236658201537},
  booktitle={Contemporary Mathematics},
  volume={747},
  year={2020},
}
Zhengwei Liu, Scott Morrison, and David Penneys. Lifting shadings on symmetrically self-dual subfactor planar algebras. 2020. Vol. 747. In Contemporary Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703162236658201537.
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