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

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.

23 pages; published version, containing the latest updates

References in corpus (4)

• Braided zesting and its applications
• Interpolated family of non group-like simple integral fusion rings of Lie type
• Triangular Prism Equations and Categorification
• On a necessary condition for unitary categorification of fusion rings

Cited by in corpus (6)

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• Interpolated family of non group-like simple integral fusion rings of Lie type
• Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories
• Structure constants, Isaacs property and Extended Haagerup fusion categories
• $G$-crossed braided zesting
• Perspectives on Anomaly Resolution