Structural Properties of The Quantized Matrix Algebra $D_q(n)$ Established by Means of Gr\"obner-Shirshov Basis Theory

TL;DR

This paper investigates the structural properties of the quantized matrix algebra $D_q(n)$ using Gr"obner-Shirshov basis theory, providing new insights into its modules and algebraic structure.

Contribution

It introduces a novel application of Gr"obner-Shirshov basis theory to analyze the algebra $D_q(n)$ and its modules, revealing new structural properties.

Findings

Structural properties of $D_q(n)$ established

Modules of $D_q(n)$ characterized

Application of Gr"obner-Shirshov basis theory demonstrated

Abstract

Let $D_q(n)$ be the quantized matrix algebra introduced by Dipper and Donkin. It is shown that some structural properties of $D_q(n)$ and their modules may be established and realized by means of Gr\"obner-Shirshov basis theory.