Set-theoretical solutions to the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability
arXiv:2203.05552 · doi:10.1134/S0040577922080074
Abstract
This paper is devoted to tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron equation. We construct a family of tetrahedron maps on associative rings. We show that matrix tetrahedron maps presented in [arXiv:2110.05998] are a particular case of our construction. This provides an algebraic explanation of the fact that the matrix maps from [arXiv:2110.05998] satisfy the tetrahedron equation. Also, Liouville integrability is established for some of the constructed maps.
8 pages. arXiv admin note: substantial text overlap with arXiv:2110.05998
References in corpus (3)
- Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
- Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation
- Boundary from bulk integrability in three dimensions: 3D reflection maps from tetrahedron maps