2 2 A ug 2 01 7 MORITA EQUIVALENCE OF POINTED FUSION CATEGORIES OF SMALL RANK
نویسنده
چکیده
We classify pointed fusion categories C(G,ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2, 2 and 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their FrobeniusSchur 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 FrobeniusSchur indicators.
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