三阶可对角化系数矩阵下Yang-Baxter矩阵方程组的解
On the Solutions to the Third-Order Yang-Baxter Matrix Equations with Diagonalizable Coefficient Matrices
DOI: 10.12677/aam.2026.154133, PDF,    科研立项经费支持
作者: 李傲楠*：赣南师范大学数学与计算机科学学院，江西 赣州；易胜辉：于都县罗江中心小学，江西 赣州
关键词: Yang-Baxter矩阵方程；Gröbner基；Jordan标准型；Yang-Baxter Matrix Equations； Gröbner Basis； Jordan Canonical Form
摘要: 本文给出了Yang-Baxter矩阵方程组在系数矩阵为三阶可对角化的情况下的解。通过对系数矩阵进行相似变换为Jordan标准型，再从解的结构出发分类讨论，使用Gröbner基技术来给出这个方程组的对应解。
Abstract: This paper investigates the solutions to the third-order Yang-Baxter matrix equations under the condition that the coefficient matrices are diagonalizable. By applying similarity transformations to reduce the coefficient matrices to their Jordan canonical forms, the structure of the solutions is analyzed through case classifications. The corresponding solutions are explicitly derived using Gröbner basis techniques.
文章引用：李傲楠, 易胜辉. 三阶可对角化系数矩阵下Yang-Baxter矩阵方程组的解[J]. 应用数学进展, 2026, 15(4): 35-41. https://doi.org/10.12677/aam.2026.154133

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