论文标题
反射方程作为研究杨巴克斯方程解决方案的工具
Reflection equation as a tool for studying solutions to the Yang-Baxter equation
论文作者
论文摘要
如果给出了Yang-Baxter方程的右非降级设置理论解决方案$（x，r）$，我们在$ x $上构建了整个YBE Solutions $ r^{（k）} $ in $ x $ index $ k $（即$ r $ reflection for Reflection for Reflection to reflection $ k $）。该家族包括原始解决方案和经典派生解决方案。所有这些解决方案都会在$ x^n $上诱导辫子组/monoid的同构作用。 $ r $和$ r^{（k）} $的结构单体与明确的$ 1 $ cocycle一样的地图相关。因此，我们将反射变成用于研究YBE解决方案的工具，而不是研究的侧面对象。在不同的方向上，我们研究了非限分涉及的YBE解决方案的反射方程，表明它等同于（任何三个更简单的关系中的任何一个，并从后者的系统构建新反射的系统方法中推断出来。
Given a right-non-degenerate set-theoretic solution $(X,r)$ to the Yang-Baxter equation, we construct a whole family of YBE solutions $r^{(k)}$ on $X$ indexed by its reflections $k$ (i.e., solutions to the reflection equation for $r$). This family includes the original solution and the classical derived solution. All these solutions induce isomorphic actions of the braid group/monoid on $X^n$. The structure monoids of $r$ and $r^{(k)}$ are related by an explicit bijective $1$-cocycle-like map. We thus turn reflections into a tool for studying YBE solutions, rather than a side object of study. In a different direction, we study the reflection equation for non-degenerate involutive YBE solutions, show it to be equivalent to (any of the) three simpler relations, and deduce from the latter systematic ways of constructing new reflections.
