Knot polynomial identities and quantum group coincidences

DOI10.4171/QT/16zbMath1239.57031arXiv1003.0022OpenAlexW3100056139MaRDI QIDQ542637

Noah Snyder, Scott Morrison, Emily Peters

Publication date: 10 June 2011

Published in: Quantum Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.0022

zbMATH Keywords

quantum groupslink invariantsknot theorymodular categoriestopological quantum field theoriesplanar algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Topological quantum field theories (aspects of differential topology) (57R56) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (12)

Quotients of representation rings ⋮ The Brauer–Picard groups of fusion categories coming from the ADE subfactors ⋮ Asymptotic behavior of integer sequences related to knots and (m,n)-anacci constants ⋮ Topological quantum field theory and polynomial identities for graphs on the torus ⋮ On constraints for knots to admit chirally cosmetic surgeries and their calculations ⋮ Webs and quantum skew Howe duality ⋮ Lie theory for fusion categories: A research primer ⋮ Drinfeld doubles of the \(n\)-rank Taft algebras and a generalization of the Jones polynomial ⋮ Categories generated by a trivalent vertex ⋮ Quadratic tangles in planar algebras ⋮ The Brauer-Picard group of the Asaeda-Haagerup fusion categories ⋮ Skein theory for the \(D_{2n}\) planar algebras

Cites Work

• Tensor products of quantized tilting modules
• Spherical categories
• Hecke algebras, modular categories and 3-manifolds quantum invariants
• Premodular categories, modularisations and invariants of 3-manifolds
• Modular categories of type \(B\), \(C\) and \(D\)

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