论文标题
杨 - 巴克斯特方程的原始设定理论解决方案
Primitive set-theoretic solutions of the Yang-Baxter equation
论文作者
论文摘要
对于有限套件上的Yang-baxter方程$ x $的每个参与的非脱位设置理论解决方案$（x，r）$，有一个自然相关的有限溶液置换组$ {\ MATHCAL G}（x，r）$在$ x $上作用。我们证明，这种类型的每个原始排列组都是Prime Order $ P $。此外，$（x，r）$是一种所谓的置换解决方案，由长度$ p $的周期确定。这解决了A. Ballester-Bolinches最近问的问题。结果对所有参与非分类设置理论解决方案的分类问题的可能方法开辟了新的观点。
To every involutive non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation on a finite set $X$ there is a naturally associated finite solvable permutation group ${\mathcal G}(X,r)$ acting on $X$. We prove that every primitive permutation group of this type is of prime order $p$. Moreover, $(X,r)$ is then a so called permutation solution determined by a cycle of length $p$. This solves a problem recently asked by A. Ballester-Bolinches. The result opens a new perspective on a possible approach to the classification problem of all involutive non-degenerate set-theoretic solutions.
