论文标题
Yang-Baxter矩阵方程系统的解决方案
Solutions to a system of Yang-Baxter matrix equations
论文作者
论文摘要
在本文中，研究了Yang-Baxter型矩阵方程的系统，$ xax = bxb $，$ xbx = axa $，它“概括”了矩阵Yang-baxter方程，并表现出破裂的对称性。我们从各种几何和拓扑观点研究了该系统的解决方案。我们分析了双随机解决方案的存在，并将解决方案交织到系统中，并描述了它们存在的条件。此外，当$ a $ a $ a和$ b $的情况是基于正交的互补的情况下，我们表征了情况。即，$ a^2 = a，b^2 = b，ab = ba = 0 $。我们还使用交换代数技术完全描述了$ n = 2 $的解决方案集。
In this article, a system of Yang-Baxter-type matrix equations is studied, $XAX=BXB$, $XBX=AXA$, which "generalizes" the matrix Yang-Baxter equation and exhibits a broken symmetry. We investigate the solutions of this system from various geometric and topological points of view. We analyze the existence of doubly stochastic solutions and intertwining solutions to the system and describe the conditions for their existence. Furthermore, we characterize the case when $A$ and $B$ are idempotent orthogonal complements. i.e., $A^2 =A, B^2= B, AB = BA =0$. We also completely characterize the set of solutions for $n=2$ using commutative algebraic techniques.
