# Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories

@inproceedings{EDIEMICHELL2021ClassificationO, title={Classification of \$\mathbb\{Z\}/2\mathbb\{Z\}\$-quadratic unitary fusion categories}, author={Cain EDIE-MICHELL and Masaki Izumi and David Penneys}, year={2021} }

A unitary fusion category is called Z/2Z-quadratic if it has a Z/2Z group of invertible objects and one other orbit of simple objects under the action of this group. We give a complete classification of Z/2Z-quadratic unitary fusion categories. The main tools for this classification are skein theory, a generalization of Ostrik’s results on formal codegrees to analyze the induction of the group elements to the center, and a computation similar to Larson’s rank-finiteness bound for Z/3Z-near…

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