Set-theoretic Yang-Baxter equation, braces and Drinfeld twists
Set-theoretic Yang-Baxter equation, braces and Drinfeld twists
复制标题
集合论 Yang-Baxter 方程、花括号和 Drinfeld 扭曲
DOI：
10.1088/1751-8121/ac219e
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Doikou A
中科院分区：
文献类型：
--
作者：
Doikou A
我们考虑Yang-Baxter方程（YBE）的对合的、非退化的有限集论解。这样的解总是可以用某些代数结构得到，这些代数结构推广了称为括号的幂零环。我们在这里的主要目的是用可接受的Drinfeld扭曲来表示这些解，这大大扩展了最近的初步结果。我们首先确定了与集合论解相关的扭转的一般形式，并证明了这些扭转是可容许的，即它们满足一定的共环条件。这些发现也适用于由集合理论解构造的YBE的bater化解。
We consider involutive, non-degenerate, finite set-theoretic solutions of the Yang–Baxter equation (YBE). Such solutions can be always obtained using certain algebraic structures that generalize nilpotent rings called braces. Our main aim here is to express such solutions in terms of admissible Drinfeld twists substantially extending recent preliminary results. We first identify the generic form of the twists associated to set-theoretic solutions and we show that these twists are admissible, ie they satisfy a certain co-cycle condition. These findings are also valid for Baxterized solutions of the YBE constructed from the set-theoretical ones.