Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation

DOI10.1088/1751-8121/ac90ffOpenAlexW3207060148MaRDI QIDQ5877072

S. Konstantinou-Rizos, Sergey Igonin

Publication date: 3 February 2023

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.05998

zbMATH Keywords

quantum Yang-Baxter equationLiouville integrabilityYang-Baxter mapsLax representationsZamolodchikov tetrahedron equationdifferentials of mapstetrahedron maps

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Matrix equations and identities (15A24) Yang-Baxter equations (16T25) Integrable difference and lattice equations; integrability tests (39A36)

Related Items (3)

Local Yang–Baxter correspondences and set-theoretical solutions to the Zamolodchikov tetrahedron equation ⋮ Birational solutions to the set-theoretical 4-simplex equation ⋮ Set-theoretical solutions to the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability

Cites Work

• Unnamed Item
• Unnamed Item
• The classification of Wada-type representations of braid groups.
• Nonlinear Schrödinger type tetrahedron maps
• Classical limits of the SU(2)-invariant solutions of the Yang-Baxter equation
• Solutions of the functional tetrahedron equation connected with the local Yang-Baxter equation for the ferro-electric condition
• Functional tetrahedron equation
• Matrix KP: tropical limit and Yang-Baxter maps
• Classification of integrable equations on quad-graphs. The consistency approach
• Boundary from bulk integrability in three dimensions: 3D reflection maps from tetrahedron maps
• Invariants in separated variables: Yang-Baxter, entwining and transfer maps
• Simplex and polygon equations.
• On non-multiaffine consistent-around-the-cube lattice equations
• Discrete Systems and Integrability
• Darboux transformations, finite reduction groups and related Yang–Baxter maps
• Multi-Quadratic Quad Equations: Integrable Cases from a Factorized-Discriminant Hypothesis
• Periodic cluster mutations and related integrable maps
• SET-THEORETIC YANG–BAXTER SOLUTIONS VIA FOX CALCULUS
• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• Integrable maps
• On some unsolved problems in quantum group theory
• Permutation-type solutions to the Yang - Baxter and othern-simplex equations
• Tetrahedron maps, Yang–Baxter maps, and partial linearisations
• Tetrahedron equation: algebra, topology, and integrability
• Non-commutative birational maps satisfying Zamolodchikov equation, and Desargues lattices
• Yang–Baxter and reflection maps from vector solitons with a boundary
• Zamolodchikov's tetrahedron equation and hidden structure of quantum groups
• Tetrahedron maps and symmetries of three dimensional integrable discrete equations
• Poisson Yang-Baxter maps with binomial Lax matrices
• Discrete KP Equation and Momentum Mapping of Toda System
• Cohomologies ofn-simplex relations
• Quantum geometry of three-dimensional lattices
• Electrical varieties as vertex integrable statistical models
• Yang–Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
• Set-theoretical solutions to the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability

This page was built for publication: Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation