Morita equivalence of pointed fusion categories of small rank

Abstract : We classify pointed fusion categories C(G, ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita equivalence classes are distinguished by the set of the indicators and ribbon twists of their Drinfeld centers. In particular, the modular data are a complete invariant for the modular categories Z(C(G, ω)) for |G[< 32. We use the computer algebra package GAP and present codes for treating complex-valued group cohomology and calculating Frobenius-Schur indicators.
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Contributeur : Michaël Mignard <>
Soumis le : jeudi 10 août 2017 - 14:24:50
Dernière modification le : jeudi 24 août 2017 - 14:34:42


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  • HAL Id : hal-01573708, version 1


Michaël Mignard, Peter Schauenburg. Morita equivalence of pointed fusion categories of small rank. 2017. <hal-01573708v1>



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