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

Zhengwei Liu Sebastien Palcoux Yunxiang Ren

Category Theory Quantum Algebra mathscidoc:2207.04004

2022.1
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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[ Download ] [ 2022-07-07 16:14:55 uploaded by Liuzhengwei ] [ 1413 downloads ] [ 0 comments ] 
@inproceedings{zhengwei2022classification,
  title={Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six},
  author={Zhengwei Liu, Sebastien Palcoux, and Yunxiang Ren},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707161455360440585},
  year={2022},
}
Zhengwei Liu, Sebastien Palcoux, and Yunxiang Ren. Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six. 2022. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707161455360440585.
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