The matched product of set-theoretical solutions of the Yang-Baxter equation
The matched product of set-theoretical solutions of the Yang-Baxter equation
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Yang-Baxter 方程集合论解的匹配积
DOI：
10.1016/j.jpaa.2019.07.012
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发表时间：
2020
影响因子：
0.8
通讯作者：
Paola Stefanelli
中科院分区：
文献类型：
--
作者：
F. Catino;I. Colazzo;Paola Stefanelli
在这项工作中，我们开发了一种新的构造技术的杨巴克斯特方程的集理论解。我们的技术，命名为匹配的产品，是一个创新的工具，以构建新的类的对合解决方案的匹配产品的两个对合解决方案仍然是对合的，反之亦然。这种方法产生新的例子的幂等解的匹配产品的其他幂等。我们翻译的上下文中的半括号，这是代数结构紧密相连的解决方案，概括了括号的Rump介绍。此外，我们证明了与两个半括号的匹配乘积相关联的解确实是与这两个半括号相关联的解的匹配乘积。
In this work, we develop a novel construction technique for set-theoretical solutions of the Yang-Baxter equation. Our technique, named the matched product, is an innovative tool to construct new classes of involutive solutions as the matched product of two involutive solutions is still involutive, and vice versa. This method produces new examples of idempotent solutions as the matched product of other idempotent ones. We translate the construction in the context of semi-braces, which are algebraic structures tightly linked with solutions that generalize the braces introduced by Rump. In addition, we show that the solution associated to the matched product of two semi-braces is indeed the matched product of the solutions associated to those two semi-braces.
动态 YangâBaxter 映射的箭袋理论方法
影响因子：
0.9
作者：
D. K. Matsumoto;K. Shimizu
通讯作者：
K. Shimizu