On the computation of fusion over the affine Temperley-Lieb algebra

DOI10.1016/J.NUCLPHYSB.2018.10.016zbMath1402.81214arXiv1802.03575OpenAlexW2786722941MaRDI QIDQ1626461

Jonathan Belletête, Yvan Saint-Aubin

Publication date: 27 November 2018

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.03575

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Continuum limits in quantum field theory (81T27) Infinite-dimensional Lie (super)algebras (17B65) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) General module theory in associative algebras (16D10)

Related Items (3)

Topological defects in lattice models and affine Temperley-Lieb algebra ⋮ Spin chains as modules over the affine Temperley-Lieb algebra ⋮ The local conserved quantities of the closed XXZ chain

Cites Work

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• The blob algebra and the periodic Temperley-Lieb algebra
• The Temperley-Lieb algebra at roots of unity
• The representation theory of affine Temperley-Lieb algebras
• The representation theory of the Temperley-Lieb algebras
• Lattice fusion rules and logarithmic operator product expansions
• Standard modules, induction and the structure of the Temperley-Lieb algebra
• Enlarged symmetry algebras of spin chains, loop models, and \(S\)-matrices
• Associative-algebraic approach to logarithmic conformal field theories
• On the algebraical braid group
• Commuting Families in Hecke and Temperley-Lieb Algebras
• The fusion rules for the Temperley–Lieb algebra and its dilute generalization
• Diagram algebras, Hecke algebras and decomposition numbers at roots of unity
• Restriction and induction of indecomposable modules over the Temperley–Lieb algebras
• Quantum invariants of knots and 3-manifolds
• Boundary algebras and Kac modules for logarithmic minimal models

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