标题： 四面体方程与代数几何 显示英文标题

标题： Tetrahedron equation and the algebraic geometry

摘要： 四面体方程作为著名的杨-巴克斯特方程推广到2+1维量子场论和三维统计力学中而出现。关于它的解，目前仍知之甚少。这里描述了一种系统的方法，可以产生非平凡的解，其中链上的自旋类变量满足四面体方程。该方法的本质是使用所谓的四面体Zamolodchikov代数。 显示英文摘要

摘要： The tetrahedron equation arises as a generalization of the famous Yang--Baxter equation to the 2+1-dimensional quantum field theory and the 3-dimensional statistical mechanics. Very little is still known about its solutions. Here a systematic method is described that does produce non-trivial solutions to the tetrahedron equation with spin-like variables on the links. The essence of the method is the use of the so-called tetrahedral Zamolodchikov algebras.