Solutions of the Yang–Baxter equation associated to skew left braces, with applications to racks
Solutions of the Yang–Baxter equation associated to skew left braces, with applications to racks
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与倾斜左括号相关的 Yang-Baxter 方程的解及其在机架上的应用
DOI：
10.1142/s0218216518500554
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发表时间：
2016
影响因子：
0.5
通讯作者：
D. Bachiller
中科院分区：
文献类型：
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作者：
D. Bachiller
给定一个斜左支撑[公式：见正文]，给出一种方法来构造杨-巴克斯特方程的所有非退化集合论解[公式：见正文]，使得相关的置换群[公式：见正文]作为斜左支撑同构于[公式：见正文]。此方法完全依赖于[Formula：see text]的大括号结构。然后，我们适应这种方法，以显示如何构建解决方案与其他属性，如平方自由，对合或不可伸缩的解决方案。使用这个结果，甚至可以从它们的置换组中恢复机架。
Given a skew left brace [Formula: see text], a method is given to construct all the non-degenerate set-theoretic solutions [Formula: see text] of the Yang–Baxter equation such that the associated permutation group [Formula: see text] is isomorphic, as a skew left brace, to [Formula: see text]. This method depends entirely on the brace structure of [Formula: see text]. We then adapt this method to show how to construct solutions with additional properties, like square-free, involutive or irretractable solutions. Using this result, it is even possible to recover racks from their permutation group.