The Standard Quantized Matrix Algebra $M_q(n)$ is A Solvable Polynomial Algebra

Let $M_q(n)$ be the standard quantized matrix algebra, introduced by Faddeev, Reshetikhin, and Takhtajan. It is shown, by constructing an appropriate monomial ordering $\prec$ on its PBW $K$-basis $\mathcal{B}$ , that $M_q(n)$ is a solvable polynomial algebra. Consequently, further structural properties of $M_q(n)$ and their modules may be established and realized in a constructive-computational way.