Some non-commuting solutions of the Yang-Baxter-like matrix equation

Some non-commuting solutions of the Yang-Baxter-like matrix equation
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类Yang-Baxter矩阵方程的一些非交换解

DOI:
10.1515/math-2020-0053
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发表时间:
2020-01
期刊:
影响因子:
1.7
通讯作者:
Vu Hong-Quang
Vu Hong-Quang
中科院分区:
数学4区
文献类型:
--
作者:
Zhou Duan-Mei;Vu Hong-Quang

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Abstract Let A be a square matrix satisfying A 4 = A {A}^{4}=A . We solve the Yang-Baxter-like matrix equation A X A = X A X AXA=XAX to find some solutions, based on analysis of the characteristic polynomial of A and its eigenvalues. We divide the problem into small cases so that we can find the solution easily. Finally, in order to illustrate the results, two numerical examples are presented.
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