Premodular categories, modularisations and invariants of 3-manifolds

DOI10.1007/s002080050011zbMath0943.18004OpenAlexW4290682826MaRDI QIDQ1971676

Alain Bruguières

Publication date: 30 August 2000

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002080050011

zbMATH Keywords

modular categorytopological quantum field theorypremodular categoryTuraev-Viro invariantReshetikhin-Turaev invariant

Mathematics Subject Classification ID

Related Items (64)

Graphs attached to simple Frobenius-Perron dimensions of an integral fusion category ⋮ Cohomology of finite tensor categories: Duality and Drinfeld centers ⋮ Galois extensions of braided tensor categories and braided crossed G-categories ⋮ Tube representations and twisting of graded categories ⋮ Fusion categories containing a fusion subcategory with maximal rank ⋮ The logarithmic Cardy case: boundary states and annuli ⋮ Dichromatic state sum models for four-manifolds from pivotal functors ⋮ Modular categories of dimension $p^3m$ with $m$ square-free ⋮ TFT construction of RCFT correlators. III: Simple currents ⋮ Representations of the necklace braid group: topological and combinatorial approaches ⋮ Braided tensor categories of admissible modules for affine Lie algebras ⋮ On the classification of the Grothendieck rings of non-self-dual modular categories ⋮ Weakly group-theoretical and solvable fusion categories ⋮ Crossed \(S\)-matrices and Fourier matrices for Coxeter groups with automorphism ⋮ Higher central charges and Witt groups ⋮ Factorizable \(R\)-matrices for small quantum groups ⋮ On the classification of weakly integral modular categories ⋮ Drinfeld centers of fusion categories arising from generalized Haagerup subfactors ⋮ \(\mathbb Z/2\mathbb Z\)-extensions of Hopf algebra module categories by their base categories ⋮ Faithful simple objects, orders and gradings of fusion categories ⋮ Drinfeld double of quantum groups, tilting modules, and \(\mathbb{Z}\)-modular data associated to complex reflection groups ⋮ \(\mathrm{SL}(2, \mathbb{Z})\)-action for ribbon quasi-Hopf algebras ⋮ Central exact sequences of tensor categories, equivariantization and applications ⋮ Metaplectic categories, gauging and property \(F\) ⋮ Lie theory for fusion categories: A research primer ⋮ Dimension as a quantum statistic and the classification of metaplectic categories ⋮ On fusion rules and solvability of a fusion category ⋮ On the extension of stringlike localised sectors in 2+1 dimensions ⋮ Solitonic sectors, \(\alpha\)-induction and symmetry breaking boundaries ⋮ Modular categories from finite crossed modules ⋮ Projections in string theory and boundary states for Gepner models. ⋮ Knot polynomial identities and quantum group coincidences ⋮ On braided fusion categories. I ⋮ Solvability of a class of braided fusion categories ⋮ Conformal orbifold theories and braided crossed \(G\)-categories ⋮ A monoidal category for perturbed defects in conformal field theory ⋮ Non-degeneracy conditions for braided finite tensor categories ⋮ Congruence subgroups and super-modular categories ⋮ The non-semisimple Verlinde formula and pseudo-trace functions ⋮ Rank-finiteness for modular categories ⋮ Braided zesting and its applications ⋮ Coring categories and Villamayor-Zelinsky sequence for symmetric finite tensor categories ⋮ Existence of Tannakian Subcategories and its Applications ⋮ Fourier matrices for \(G(d,1,n)\) from quantum general linear groups ⋮ Mathematics of topological quantum computing ⋮ On classification of super-modular categories of rank 8 ⋮ Line and surface defects in Reshetikhin-Turaev TQFT ⋮ On classification of modular tensor categories ⋮ The small quantum group as a quantum double ⋮ TFT construction of RCFT correlators. I: Partition functions ⋮ Orbifold aspects of the Longo--Rehren subfactors ⋮ A spin decomposition of the verlinde formulas for type A modular categories ⋮ Double braidings, twists and tangle invariants ⋮ Correspondences of ribbon categories ⋮ Domain walls between 3d phases of Reshetikhin-Turaev TQFTs ⋮ Classification of rank 5 premodular categories ⋮ On odd-dimensional modular tensor categories ⋮ Quantum groups and ribbon \(G\)-categories ⋮ Jones-Witten invariants for nonsimply connected Lie groups and the geometry of the Weyl alcove ⋮ Invariants of spin three-manifolds from Chern-Simons theory and finite-dimensional Hopf algebras ⋮ On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories ⋮ Modular categories with transitive Galois actions ⋮ From torus bundles to particle-hole equivariantization ⋮ From subfactors to categories and topology. II: The quantum double of tensor categories and subfactors

This page was built for publication: Premodular categories, modularisations and invariants of 3-manifolds