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

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 G...

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Bibliographic Details
Published in:Letters in mathematical physics 2022-06, Vol.112 (3), Article 54
Main Authors: Liu, Zhengwei, Palcoux, Sebastien, Ren, Yunxiang
Format: Article
Language:English
Subjects:
Algebra
Categories
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-022-01542-1