Let  be the quadratic matrix algebra associated to the quantized enveloping algebra  It is shown explicitly that the defining relations of  form a Gröbner-Shirshov basis. Consequently, several structural properties of  are derived.

quadratic matrix algebra, Gröbner-Shirshov basis, PBW basis.

Received: June 13, 2023; Accepted: July 21, 2023; Published: September 1, 2023

How to cite this article: Lina Niu and Rabigul Tuniyaz, Some structural properties of the quantized matrix algebra  JP Journal of Algebra, Number Theory and Applications 62(1) (2023), 71-86. http://dx.doi.org/10.17654/0972555523022

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