论文标题
在杨 - 巴克斯特方程的派生不合格解决方案上
On derived-indecomposable solutions of the Yang--Baxter equation
论文作者
论文摘要
如果$（x，r）$是Yang-baxter方程的有限的非脱位设定理论解决方案，则结构偏斜支撑$ G（x，r）$的添加群是一个$ FC $ -Group，即其元素有很多结合物的组。此外，它的乘法组几乎是Abelian，因此它也接近$ FC $ - 组本身。如果一个人还假设$（x，r）$的派生解决方案是不可兼容的，那么对于$ g（x，r）$的每个元素$ b $ of $ b $ of $ b $ of $ b*c $ b*c $ and $ c*b $有限的许多元素，in G（x，r）$。这自然会导致研究$ fc $ groups类的支架理论类似物。对于这类偏斜的牙套，描述了基本结果及其与YBE解决方案的联系：我们证明它们具有良好的扭转和激进理论，并且在某些nilpotency概念和有限的产生方面，它们的行为很好。
If $(X,r)$ is a finite non-degenerate set-theoretic solution of the Yang--Baxter equation, the additive group of the structure skew brace $G(X,r)$ is an $FC$-group, i.e. a group whose elements have finitely many conjugates. Moreover, its multiplicative group is virtually abelian, so it is also close to an $FC$-group itself. If one additionally assumes that the derived solution of $(X,r)$ is indecomposable, then for every element $b$ of $G(X,r)$ there are finitely many elements of the form $b*c$ and $c*b$, with $c\in G(X,r)$. This naturally leads to the study of a brace-theoretic analogue of the class of $FC$-groups. For this class of skew braces, the fundamental results and their connections with the solutions of the YBE are described: we prove that they have good torsion and radical theories and they behave well with respect to certain nilpotency concepts and finite generation.
