论文标题
偏斜支架的根本和重量及其在结构Yang-baxter方程解决方案组的组组中的应用
Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation
论文作者
论文摘要
我们定义了偏斜左支架的根本和重量，并提供了这些概念的一些基本特性。特别是，我们获得了Artinian偏斜左括号的Wedderburn型分解。此外，我们证明了Wiegold定理的类似物，Schur的定理及其在偏斜的左括号的背景下。最后，我们将这些结果应用于检测有限的Yang-Baxter方程中有限的非脱位式理论解的结构组中的扭转。
We define the radical and weight of a skew left brace and provide some basic properties of these notions. In particular, we obtain a Wedderburn type decomposition for Artinian skew left braces. Furthermore, we prove analogues of a theorem of Wiegold, a theorem of Schur and its converse in the context of skew left braces. Finally, we apply these results to detect torsion in the structure group of a finite bijective non-degenerate set-theoretic solution of the Yang-Baxter equation.
