Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems

DOI10.1016/j.physd.2022.133466OpenAlexW4288809982WikidataQ113866727 ScholiaQ113866727MaRDI QIDQ2083724

S. Konstantinou-Rizos

Publication date: 11 October 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.10491

zbMATH Keywords

Darboux transformationsmatrix six-factorisation problemnoncommutative NLS type tetrahedron mapsnoncommutative Sergeev's mapnoncommutative tetrahedron mapsZamolodchikov's functional tetrahedron equation

Mathematics Subject Classification ID

Operator theory (47-XX) Difference and functional equations (39-XX)

Related Items (3)

Parametric 4-simplex maps of degenerated NLS type ⋮ Local Yang–Baxter correspondences and set-theoretical solutions to the Zamolodchikov tetrahedron equation ⋮ Birational solutions to the set-theoretical 4-simplex equation

Cites Work

• Families of integrable equations
• Non-commutative rational Yang-Baxter maps
• Nonlinear Schrödinger type tetrahedron maps
• The Yang-Baxter equations and the Zamolodchikov model
• Solutions of the functional tetrahedron equation connected with the local Yang-Baxter equation for the ferro-electric condition
• Functional tetrahedron equation
• Relativistic collisions as Yang-Baxter maps
• Integrable noncommutative equations on quad-graphs. The consistency approach
• A discrete Darboux-Lax scheme for integrable difference equations
• The Coxeter relations and KP map for non-commuting symbols
• Simplex and polygon equations.
• On non-multiaffine consistent-around-the-cube lattice equations
• Burgers and Kadomtsev-Petviashvili hierarchies: a functional representation approach
• The discrete and continuous Painlevé VI hierarchy and the Garnier systems
• Yang–Baxter maps with first-degree-polynomial 2 × 2 Lax matrices
• On non-abelian quadrirational Yang–Baxter maps*
• Tetrahedron maps, Yang–Baxter maps, and partial linearisations
• Tetrahedron equation: algebra, topology, and integrability
• Algebraic Structures in Integrability
• Non-commutative birational maps satisfying Zamolodchikov equation, and Desargues lattices
• Poisson structures for lifts and periodic reductions of integrable lattice equations
• Zamolodchikov's tetrahedron equation and hidden structure of quantum groups
• Tetrahedron maps and symmetries of three dimensional integrable discrete equations
• On a non-Abelian Hirota–Miwa equation
• The direct linearisation approach to hierarchies of integrable PDEs in 2 + 1 dimensions: I. Lattice equations and the differential-difference hierarchies
• Quantum geometry of three-dimensional lattices
• Unnamed Item
• Unnamed Item

This page was built for publication: Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems