2017/08/22 by Michaël Mignard, Peter Schauenburg, Mignard, Michaël +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1708.06538
openalex publication_date 2017/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.