Modular invariants for group-theoretical modular data. I

2009/08/07 by Alexei Davydov, Davydov, Alexei · 3 citations
Mathematics · #18D10 #18D35 #81R50 #81T40 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.0908.1044

openalex publication_date 2009/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify indecomposable commutative separable (special Frobenius) algebras and their local modules in (untwisted) group-theoretical modular categories. This gives a description of modular invariants for group-theoretical modular data. As a bi-product we provide an answer to the question when (and in how many ways) two group-theoretical modular categories are equivalent as ribbon categories.

Citations

• From subfactors to categories and topology II: The quantum double of tensor categories and subfactors
• On the Structure of Modular Categories
• Isocategorical groups

Cited by

• Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes
• Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants
• The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed-State SPTs

Related

• Modular categories are not determined by their modular data
• Modular data of non-semisimple modular categories
• Constructing non-semisimple modular categories with local modules
• On invariants of Modular categories beyond modular data
• Constructing modular categories from orbifold data