Quantum groups, quantum categories and quantum field theory

zbMath0789.17005MaRDI QIDQ686869

Thomas Kerler, Jürg Fröhlich

Publication date: 10 October 1993

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

irreducible representationmonoidal categoriesuniqueness theoremquantum groupssuperselection sectorsquantum field theoriesfusion rule algebrasquasitensor category

Mathematics Subject Classification ID

Related Items (40)

Theory of superselection sectors for generalized Ising models ⋮ On Frobenius-Perron dimension ⋮ Galois extensions of braided tensor categories and braided crossed G-categories ⋮ Construction of field algebras with quantum symmetry from local observables ⋮ The quantum symmetry of rational field theories ⋮ Higher-dimensional algebra. II: 2-Hilbert spaces ⋮ The Brauer–Picard groups of fusion categories coming from the ADE subfactors ⋮ TFT construction of RCFT correlators. III: Simple currents ⋮ On extensions of two families of Tambara–Yamagami categories ⋮ Categorical extensions of conformal nets ⋮ Operator realization of the SU(2) WZNW model ⋮ Classification of pivotal tensor categories with fusion rules related to \(SO(4)\) ⋮ The CPT and Bisognano-Wichmann theorems for anyons and plektons in \(d=2+1\) ⋮ PI degree of quantized Weyl algebras ⋮ Some structure theory of table algebras and applications to association schemes ⋮ Near-group categories ⋮ Sylow theory for table algebras, fusion rule algebras, and hypergroups. ⋮ Metaplectic categories, gauging and property \(F\) ⋮ Preface ⋮ On the universal \(R\)-matrix for \(U_ q(sl_{r+1})\) ⋮ On second quantization of quantum groups ⋮ Permutation modules over table algebras and applications to association schemes. ⋮ Nilpotent fusion categories ⋮ Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model ⋮ Decomposition of products in nilpotent table algebras. ⋮ Conformal correlation functions, Frobenius algebras and triangulations ⋮ Entropic order parameters for the phases of QFT ⋮ Braiding structures on formal Poisson groups and classical solutions of the QYBE. ⋮ Topological representations of the quantum group \(U_ q(sl_ 2)\) ⋮ Classifying fusion categories \(\otimes\)-generated by an object of small Frobenius-Perron dimension ⋮ On braided almost square-free fusion categories with odd dimension ⋮ Table algebras ⋮ On classification of modular tensor categories ⋮ TFT construction of RCFT correlators. I: Partition functions ⋮ Tannaka duals in semisimple tensor categories ⋮ Extensions of a near-group category of type \((\mathbb{Z}_2;1)\) ⋮ The automorphisms of affine fusion rings. ⋮ Topological representations of \(U_ q(\text{sl}_ 2(\mathbb{C}))\) on the torus and the mapping class group ⋮ Modular categories with transitive Galois actions ⋮ A remark on CFT realization of quantum doubles of subfactors: case index \(<4\)

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