Skein theory for the \(ADE\) planar algebras

DOI10.1016/j.jpaa.2009.07.010zbMath1192.46059arXiv0903.0144OpenAlexW2964247513MaRDI QIDQ847155

Stephen J. Bigelow

Publication date: 12 February 2010

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.0144

zbMATH Keywords

relationsgeneratorsplanar algebras\(E_{8}\) subfactor

Mathematics Subject Classification ID

Relations of low-dimensional topology with graph theory (57M15) Subfactors and their classification (46L37) Methods of category theory in functional analysis (46M99)

Related Items (11)

The Brauer–Picard groups of fusion categories coming from the ADE subfactors ⋮ The state sum invariant of 3-manifolds constructed from the \(E_{6}\) linear skein ⋮ Web bases for the general linear groups ⋮ 2-supertransitive subfactors at index \(3 + \sqrt{5}\) ⋮ The classification of subfactors of index at most 5 ⋮ Subfactors of index less than 5. III: Quadruple points ⋮ Universal skein theory for finite depth subfactor planar algebras ⋮ Constructing the extended Haagerup planar algebra ⋮ Skein theory for the \(D_{2n}\) planar algebras ⋮ Classification of Thurston relation subfactor planar algebras ⋮ An elementary proof of a non-triviality of the E₈subfactor planar algebra

Cites Work

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• Quadratic tangles in planar algebras
• Skein theory for the \(D_{2n}\) planar algebras
• Application of fusion rules to classification of subfactors
• On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
• Spiders for rank 2 Lie algebras

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