\(sl(N)\) Onsager's algebra and integrability

DOI10.1007/BF02189226zbMath1260.82011arXivhep-th/9502068OpenAlexW2047593281MaRDI QIDQ1946917

Uglov D. B., Ivan T. Ivanov

Publication date: 10 April 2013

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9502068

zbMATH Keywords

loop algebrasOnsager's algebraIsing model integrability

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Quantum equilibrium statistical mechanics (general) (82B10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Irreversible thermodynamics, including Onsager-Machlup theory (82B35) Lattice dynamics; integrable lattice equations (37K60)

Related Items (13)

Deformed Dolan-Grady relations in quantum integrable models ⋮ The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra ⋮ Quantum spin chains from Onsager algebras and reflection \(K\)-matrices ⋮ Generalized Onsager algebras ⋮ Vertex ring-indexed Lie algebras ⋮ Irreducible finite-dimensional representations of equivariant map algebras ⋮ Higher order relations for ADE-type generalized \(q\)-Onsager algebras ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other ⋮ FRT presentation of the Onsager algebras ⋮ Higher rank classical analogs of the Askey-Wilson algebra from the sl_N Onsager algebra ⋮ Defining relations for quantum symmetric pair coideals of Kac-Moody type ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ The Askey–Wilson algebra and its avatars

Cites Work

• Unnamed Item
• Cyclic \(L\)-operator related with a 3-state \(R\)-matrix
• Spectrum and completeness of the three-state superintegrable chiral Potts model
• The statistics of dimers on a lattice
• Onsager’s algebra and the Dolan–Grady condition in the non-self-dual case
• Onsager's algebra and superintegrability
• Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

This page was built for publication: \(sl(N)\) Onsager's algebra and integrability