论文标题
Zamolodchikov四面体方程的设定理论解决方案和Liouville的集成性
Set-theoretical solutions to the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability
论文作者
论文摘要
本文致力于四面体图，这些图是Zamolodchikov四面体方程的理论解决方案。我们在关联环上构建了四面体图的家族。我们表明，[Arxiv：2110.05998]中介绍的矩阵四面体图是我们构造的一种特殊情况。这提供了一个代数解释，即[arxiv：2110.05998]的矩阵映射满足四面体方程。另外，为某些构建的地图建立了Liouville的集成性。
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.
