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arXiv · 2010.10264

Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six

Zhengwei Liu·Sebastien Palcoux·Yunxiang Ren
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Abstract

This paper classifies the Grothendieck rings of complex fusion categories of multiplicity one up to rank six. Among 72 possible fusion rings, $25$ ones are filtered out by using categorification criteria. Each of the remaining 47 fusion rings admits a unitary complex categorification. We found 6 new Grothendieck rings, categorified by applying a localization approach of the Pentagon Equation.

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Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren. 2022-06-05. Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six. https://doi.org/10.1007/s11005-022-01542-1

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