Structural properties of the quantized matrix algebra \(D_q (n)\) established by means of Gröbner-Shirshov basis theory (Q6580181)

This paper considers structural properties of the quantized matrix algebra \(D_q(n)\) (introduced by \textit{R. Dipper} and \textit{S. Donkin} [Proc. Lond. Math. Soc. (3) 63, No. 1, 165--211 (1991; Zbl 0734.20018)]) by means of Gröbner-Shirshov basis theory. It is shown that \(D_q(n)\) has a PBW-basis and that it is a solvable polynomial algebra. Several applications of the above results are also given in this article.