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Morita equivalence of pointed fusion categories of small rank (1708.06538v1)
Published 22 Aug 2017 in math.QA, math.CT, and math.RT
Abstract: We classify pointed fusion categories C(G, $\omega$) 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, $\omega$)) for |G[< 32. We use the computer algebra package GAP and present codes for treating complex-valued group cohomology and calculating Frobenius-Schur indicators.