A Gram determinant for Lickorish's bilinear form

DOI10.1017/S0305004111000089zbMath1229.57013arXiv1006.1297MaRDI QIDQ3006531

Xuanting Cai

Publication date: 20 June 2011

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.1297

zbMATH Keywords

surfacebasisTemperley-Lieb algebraskein theorylink diagram3-manifold invariantsGram determinantKaufmann bracketLickorish's bilinear form

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Braid groups; Artin groups (20F36) Topological quantum field theories (aspects of differential topology) (57R56)

Related Items (5)

Dual bases in Temperley-Lieb algebras, quantum groups, and a question of Jones ⋮ A generalization of the Gram determinant of type A ⋮ A note on fully commutative elements in complex reflection groups ⋮ A cellular basis for the generalized Temperley-Lieb algebra and Mahler measure ⋮ Bilinear forms on skein modules and steps in Dyck paths

Cites Work

• A combinatorial matrix in 3-manifold theory
• Invariants for 3-manifolds from the combinatorics of the Jones polynomial
• The Gram determinant of the type B Temperley-Lieb algebra
• Quantum field theory and the Jones polynomial
• A calculus for framed links in \(S^3\)
• Meander determinants
• Skeins and handlebodies
• 3-valent graphs and the Kauffman bracket
• Meanders and the Temperley-Lieb algebra
• Topological quantum field theories derived from the Kauffman bracket
• Invariants of 3-manifolds via link polynomials and quantum groups
• Explicit diagonalization of the Markov form on the Temperley–Lieb algebra

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