THE GENERALIZED YANG-BAXTER MATRIX EQUATION $$ A(XA)^{m}=X(AX)^{m} $$ OVER $$ \textrm{GL}(2,\mathbb {F}) $$
Boaz Cohen · Journal of Mathematical Sciences · 2025
Abstract Let A be a given $$ 2\times 2 $$ 2 × 2 non-singular matrix over a general field $$ \mathbb {F} $$ F , and let m be an arbitrary positive integer. In this article, we completely solve the generalized Yang-Baxter matrix equation, namely the equation $$ A(XA)^{m}=X(AX)^{m} $$ A ( X A ) m = X ( A X ) m for the unknown non-singular matrix X .