Computing Modular Data for Pointed Fusion Categories

2018/08/15 by Gruen, Angus, Morrison, Scott · 4 citations
#18-04 (Secondary) #18D10 (Primary) #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1808.05060

Abstract

A formula for the modular data of Z(Vec^ωG) was given by Coste, Gannon and Ruelle in arXiv:hep-th/0001158, but without an explicit proof for arbitrary 3-cocycles. This paper presents a derivation using the representation category of the quasi Hopf algebra D^ωG. Further, we have written code to compute this modular data for many pairs of small finite groups and 3-cocycles. This code is optimised using Galois symmetries of the S and T matrices. We have posted a database of modular data for the Drinfeld center of every Morita equivalence class of pointed fusion categories of dimension less than 64.

Cited by

• Modular fusion categories with few twists
• Morita invariants of quasitriangular comodule algebras
• Classifying integral Grothendieck rings up to rank 5 and beyond
• SymTFT Approach for Mixed States with Non-Invertible Symmetries

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