Structural properties of the quantized matrix algebra \(D_q (n)\) established by means of Gröbner-Shirshov basis theory (Q6580181)
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scientific article; zbMATH DE number 7888149
| Language | Label | Description | Also known as |
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| English | Structural properties of the quantized matrix algebra \(D_q (n)\) established by means of Gröbner-Shirshov basis theory |
scientific article; zbMATH DE number 7888149 |
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Structural properties of the quantized matrix algebra \(D_q (n)\) established by means of Gröbner-Shirshov basis theory (English)
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29 July 2024
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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.
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quantized matrix algebra
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Gröbner-Shirshov basis
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solvable polynomial algebra
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