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

被引：0
|
作者：
Zhengwei Liu
Sebastien Palcoux
Yunxiang Ren
机构：
[1] Tsinghua University,Department of Mathematics, Yau Mathematical Sciences Center
[2] Beijing Institute of Mathematical Sciences and Applications,Department of Physics
[3] Harvard University,undefined
来源：
Letters in Mathematical Physics | 2022年 / 112卷
关键词：
Fusion ring; Grothendieck ring; Fusion category; Categorification; Classification; Multiplicity-free; 18M20;
D O I：
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学科分类号：
摘要：
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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