标题： 所有量子Yang-Baxter方程的4x4解 显示英文标题

标题： All 4 x 4 solutions of the quantum Yang-Baxter equation

摘要： 本文中，我们完成了4×4 Yang-Baxter方程解的分类。 正则解最近已被分类，而在本文中我们找到了剩余的非正则解。 我们呈现了若干新的解，然后考虑正则和非正则Lax算子，并研究它们与量子Yang-Baxter方程的关系。 我们展示了对于正则解存在一种对应关系，在非正则情况下这种对应关系丢失。 特别是，我们发现了非正则Lax算子，其R矩阵从基本交换关系中是正则的，但不满足Yang-Baxter方程。 这些R矩阵转而满足修改后的Yang-Baxter方程。 显示英文摘要

摘要： In this paper, we complete the classification of 4 x 4 solutions of the Yang-Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang-Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R-matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R-matrices satisfy a modified Yang-Baxter equation instead.