Structural properties of the quantized matrix algebra \(D_q (n)\) established by means of Gröbner-Shirshov basis theory
type: Item
instance of: scholarly article
title: Structural properties of the quantized matrix algebra \(D_q (n)\) established by means of Gröbner-Shirshov basis theory
author: Li'na Niu
author: Rabigul Tuniyaz
published in: Journal of Algebra and its Applications
publication date: 2024-07-29T00:00:00Z
review text: 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.
reviewed by: Xiangui Zhao
Mathematics Subject Classification ID: 16Z10
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 7888149
zbMATH Keywords: quantized matrix algebra
zbMATH Keywords: Gröbner-Shirshov basis
zbMATH Keywords: solvable polynomial algebra
MaRDI profile type: Publication
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DOI: 10.1142/S0219498825500574
description: scientific article; zbMATH DE number 7888149