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arXiv · 2609.33272

Grothendieck rings of pivotal fusion categories of rank four

Jingcheng Dong·Sebastien Palcoux·Arnaud Plessis
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Abstract

We classify the Grothendieck rings of pivotal fusion categories of rank four over the complex numbers. There are exactly fifteen, each admitting a unitary categorification. Central induction and Frobenius-Schur indicators give a uniform Frobenius-Perron dimension bound of 3600. The finite classification combines new arithmetic and twist obstructions with an exhaustive census and exact exclusion certificates.

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Jingcheng Dong, Sebastien Palcoux, Arnaud Plessis. 2026-09-27. Grothendieck rings of pivotal fusion categories of rank four. https://arxiv.org/abs/2609.33272

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