Set-theoretical solutions to the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability

DOI10.1134/S0040577922080074zbMath1516.37126arXiv2203.05552OpenAlexW4226197594MaRDI QIDQ6393373

S. A. Igonin

Publication date: 10 March 2022

Full work available at URL: https://doi.org/10.1134/s0040577922080074

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Lattice dynamics; integrable lattice equations (37K60) Yang-Baxter equations (16T25) Integrable difference and lattice equations; integrability tests (39A36)

Related Items

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

Cites Work

• Solutions of the functional tetrahedron equation connected with the local Yang-Baxter equation for the ferro-electric condition
• Functional tetrahedron equation
• Boundary from bulk integrability in three dimensions: 3D reflection maps from tetrahedron maps
• Darboux transformations, finite reduction groups and related Yang–Baxter maps
• Periodic cluster mutations and related integrable maps
• Integrable maps
• Tetrahedron equation: algebra, topology, and integrability
• Non-commutative birational maps satisfying Zamolodchikov equation, and Desargues lattices
• Zamolodchikov's tetrahedron equation and hidden structure of quantum groups
• Tetrahedron maps and symmetries of three dimensional integrable discrete equations
• Cohomologies ofn-simplex relations
• Quantum geometry of three-dimensional lattices
• Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation