Modular categories are not determined by their modular data

Modular categories are not determined by their modular data

Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular categories.

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Veröffentlicht in:Letters in mathematical physics 2021-06, Vol.111 (3), Article 60
Hauptverfasser: Mignard, Michaël, Schauenburg, Peter
Format: Artikel
Sprache:eng
Schlagworte:
Categories
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Beschreibung
Zusammenfassung:Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular categories.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01395-0