论文标题
来自立方体复合物的杨 - 巴克斯特方程的Drinfeld-Manin溶液
Drinfeld-Manin solutions of the Yang-Baxter equation coming from cube complexes
论文作者
论文摘要
杨手机方程最常见的几何解释是辫子，结和相关的雷迪德移动。到目前为止，只使用第三个雷迪德移动的立方体用于连接。我们将证明，有更高维度的立方体综合体解决了任意大的$ d $的$ d $ state yang-baxter方程。更确切地说，我们引入了由$ N $ TROOD产品覆盖的Cube Complexs的明确结构，并表明这些Cube综合体导致了Yang-Baxter方程的新解决方案。
The most common geometric interpretation of the Yang-Baxter equation is by braids, knots and relevant Reidemeister moves. So far, cubes were used for connections with the third Reidemeister move only. We will show that there are higher-dimensional cube complexes solving the $D$-state Yang-Baxter equation for arbitrarily large $D$. More precisely, we introduce explicit constructions of cube complexes covered by products of $n$ trees and show that these cube complexes lead to new solutions of the Yang-Baxter equations.
