On the projection-based commuting solutions of the Yang-Baxter matrix equation

被引：11
|
作者：
Zhou, Duanmei [1 ]
Chen, Guoliang [2 ]
Yu, Gaohang [1 ]
Zhong, Jian [1 ]
机构：
[1] Gannan Normal Univ, Coll Math & Comp Sci, Ganzhou 341000, Peoples R China
[2] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2018年 / 79卷
基金：
中国国家自然科学基金;
关键词：
Projection; Eigenvalues; Yang-Baxter equation; Jordan form; SPECTRAL SOLUTIONS;
D O I：
10.1016/j.aml.2017.12.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the commuting solutions of the Yang-Baxter matrix equation AXA = XAX when A is an arbitrary square matrix. By characterizing its commuting solutions based on projection matrices, we show that projections can be determined by using the generalized eigenspaces corresponding to the eigenvalues of A. Therefore, commuting solutions can be constructed explicitly. Our results are more general than those obtained recently by Dong (2017), Ding and Zhang (2014), and Ding and Rhee (2013). (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：155 / 161
页数：7
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