.svg){kind=logo}
SOME STRUCTURAL PROPERTIES OF THE QUANTIZED MATRIX ALGEBRA $J_q^z(n)$
(Dedicated to Professor Abdukadir Obul on the Occasion of his 60th Birthday)
Keywords:
quadratic matrix algebra, Gröbner-Shirshov basis, PBW basis.DOI:
https://doi.org/10.17654/0972555523022Abstract
Let $J_q^z(n)$ be the quadratic matrix algebra associated to the quantized enveloping algebra $U_q\left(A_{2 n-1}\right)$. It is shown explicitly that the defining relations of $J_q^z(n)$ form a Gröbner-Shirshov basis. Consequently, several structural properties of $J_q^z(n)$ are derived.
Received: June 13, 2023
Accepted: July 21, 2023
References
L. Bokut et al., Gröbner-Shirshov Bases: Normal Forms, Combinatorial and Decision Problems in Algebra, World Scientific Publishing, 2020.
H. P. Jakobsen and H. Zhang, A class of quadratic matrix algebras arising from the quantized enveloping algebra J. Math. Phys. 41 (2000), 2310-2336.
H. Li, An elimination lemma for algebras with PBW bases, Communications in Algebra 46(8) (2018), 3520-3532.
H. Li, Noncommutative Polynomial Algebras of Solvable Type and their Modules: Basic Constructive-computational Theory and Methods, Chapman and Hall/CRC Press, 2021.
H. Li, Gröbner Bases in Ring Theory, World Scientific Publishing Co., 2011. https://doi.org/10.1142/8223.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
