论文标题
Zamolodchikov的四面体方程和矩阵六面构造问题的非共同解决方案
Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems
论文作者
论文摘要
众所周知，局部杨 - 巴克斯特方程是Zamolodchikov的四面体方程的潜在解决方案的发生器。在本文中，我们在哪些条件下表明了局部杨的解决方案 - 巴克斯特方程是四面体图，即对集合理论四面体方程的解决方案。当一个人想证明非交通映射满足Zamolodchikov的四面体方程时，这非常有用。我们构建了新的非交通图，并证明它们具有四面体特性。此外，通过使用非交通变量的Darboux转换，我们得出了非交通性的四面体图。特别是，我们得出了四面体映射的非交互性非线性schrödinger类型，该类型可以限于Sergeev在不变叶子上的Sergeev地图的非交换版本。我们证明这些地图是四面体图。
It is known that the local Yang--Baxter equation is a generator of potential solutions to Zamolodchikov's tetrahedron equation. In this paper, we show under which additional conditions the solutions to the local Yang--Baxter equation are tetrahedron maps, namely solutions to the set-theoretical tetrahedron equation. This is exceptionally useful when one wants to prove that noncommutative maps satisfy the Zamolodchikov's tetrahedron equation. We construct new noncommutative maps and we prove that they possess the tetrahedron property. Moreover, by employing Darboux transformations with noncommutative variables, we derive noncommutative tetrahedron maps. In particular, we derive a noncommutative nonlinear Schrödinger type of tetrahedron map which can be restricted to a noncommutative version of Sergeev's map on invariant leaves. We prove that these maps are tetrahedron maps.
