论文标题
构建杨巴克斯特方程的有限简单解决方案
Constructing finite simple solutions of the Yang-Baxter equation
论文作者
论文摘要
我们研究有限集X上阳式方程的参考非分类理论解决方案（x，r）。重点是在（（x，r）是不可塑性的情况下，因此相关的置换组在X上具有固定性作用。以及如何表征这些块。我们专注于所谓的简单解决方案，这是至关重要的。第一次建造了几个无限的解决方案家族。特别是，对于任何prime p，一类简单的顺序p^2解决方案都是完全表征的。
We study involutive non-degenerate set-theoretic solutions (X,r) of the Yang-Baxter equation on a finite set X. The emphasis is on the case where (X,r) is indecomposable, so the associated permutation group acts transitively on X. One of the major problems is to determine how such solutions are built from the imprimitivity blocks; and also how to characterize these blocks. We focus on the case of so called simple solutions, which are of key importance. Several infinite families of such solutions are constructed for the first time. In particular, a broad class of simple solutions of order p^2, for any prime p, is completely characterized.
