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Classifying Grothendieck rings of pivotal fusion categories of rank four
Abstract
We classify the Classifying Grothendieck rings of pivotal fusion categories of rank four over the complex field. 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.
Related
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BibTeX
@misc{dong2026classifying,
title = {{Classifying Grothendieck rings of pivotal fusion categories of rank four}},
author = {Jingcheng Dong and Sebastien Palcoux and Arnaud Plessis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.33272},
eprint = {2609.33272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33272},
}
RIS
TY - UNPB
TI - Classifying Grothendieck rings of pivotal fusion categories of rank four
AU - Jingcheng Dong
AU - Sebastien Palcoux
AU - Arnaud Plessis
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.33272
UR - https://arxiv.org/abs/2609.33272
AB - We classify the Classifying Grothendieck rings of pivotal fusion categories of rank four over the complex field. 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.
ER -