From subfactors to categories and topology II: The quantum double of tensor categories and subfactors

2003/03/25 by Michael Müger · 356 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Algebraically closed field #Center (category theory) #Closed monoidal category #Discrete mathematics #Equivalence of categories #Functor #Homotopy and Cohomology in Algebraic Topology #Hopf algebra #Invertible matrix #Isomorphism (crystallography) #Mathematics #Monoidal category #Morphism #Pure mathematics #Simple (philosophy) #Simple module #Symmetric monoidal category #Tensor (intrinsic definition) #Zero (linguistics)

paper · pdf · doi:10.1016/s0022-4049(02)00248-7

published in Journal of Pure and Applied Algebra 180(1-2), 159-219 (Elsevier BV)

openalex publication_date 2003/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• The monoidal center and the character algebra
• Parafermionizing the Monster
• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers
• String-net model of Turaev-Viro invariants
• Jones-Wassermann subfactors for modular tensor categories
• Relative center construction for G-graded C^*-tensor categories and Longo-Rehren inclusions
• On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs
• Topological Quantum Field Theories from Compact Lie Groups
• Stacking and the triviality of invertible phases
• The braided monoidal structure of tube algebra representations
• Generalized Witt and Morita equivalences
• Generalized and quasi-localizations of braid group representations
• Algebraic number fields generated by Frobenius-Perron dimensions in fusion rings
• Fully local Reshetikhin-Turaev theories
• Linear effects, exceptions, and resource safety: a Curry-Howard correspondence for destructors
• Compactification of quasi-local algebras on the lattice
• Topological Quantum
• On two approaches to 3-dimensional TQFTs
• Orbifolds and minimal modular extensions
• Finite generation of cohomology for Drinfeld doubles of finite group schemes
• On the center of fusion categories
• On fusion categories
• On braided fusion categories I
• Generalized Symmetries From Fusion Actions
• Simple transitive 2-representations and Drinfeld center for some finitary 2-categories
• Categorical Anomaly Matching
• Unipotent representations as a categorical centre
• Modular invariants for group-theoretical modular data. I
• Symmetry, Symmetry Topological Field Theory and von Neumann Algebra
• Conformal Net Realizability of Tambara-Yamagami Categories and Generalized Metaplectic Modular Categories
• The core of a weakly group-theoretical braided fusion category
• Block maps and Fourier analysis
• Frobenius-Schur indicators in Tambara-Yamagami categories
• Kitaev's Lattice Model and Turaev-Viro TQFTs
• Commutative Algebras in Fibonacci Categories
• Turaev-Viro invariants as an extended TQFT
• The Elliptic Drinfeld Center of a Premodular Category
• Pairing and Quantum Double of Finite Hopf C*-Algebras
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• On formal codegrees of fusion categories
• Semisimple and separable algebras in multi-fusion categories
• Truncated convolution of character sheaves
• Categorical quantum volume operator
• On 3-dimensional homotopy quantum field theory III: comparison of two approaches
• Finitely semisimple spherical categories and modular categories are self-dual
• Group-theoretical properties of nilpotent modular categories
• From Quantum Groups to Unitary Modular Tensor Categories
• Non-invertible symmetry enriched string net topological orders
• Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids
• Cardy algebras and sewing constraints, II
• Modular fusion categories with trivial Torelli group actions
• Theory of twist liquids: Gauging an anyonic symmetry
• The Ponzano–Regge model
• Higgsing Transitions from Topological Field Theory & Non-Invertible Symmetry in Chern-Simons Matter Theories
• Drinfeld Center and Representation Theory for Monoidal Categories
• Quantum computation with Turaev–Viro codes
• Integrability and Braided Tensor Categories
• Integral transforms and Drinfeld centers in derived algebraic geometry
• On the structure of DHR bimodules of abstract spin chains
• Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility