Morita equivalence of pointed fusion categories of small rank

Michaël Mignard (1) , Peter Schauenburg (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: Fusion category; Modular category

Domaines: Algèbres quantiques [math.QA]; Catégories et ensembles [math.CT]; Théorie des représentations [math.RT]

Michaël Mignard, Peter Schauenburg. Morita equivalence of pointed fusion categories of small rank. 2017. ⟨hal-01573708v2⟩