On The Algebras $U_q^{\pm}(A_N)$: From A Constructive-Computational Viewpoint

Rabigul Tuniyaz

paper

On The Algebras $U_{q}^{\pm} (A_{N})$ : From A Constructive-Computational Viewpoint

arXiv:2202.02793

Abstract

Let $U_{q}^{+} (A_{N})$ (resp. $U_{q}^{-} (A_{N})$ ) be the $(+)$ -part (resp. $(-)$ -part) of the Drinfeld-Jimbo quantum group of type $A_{N}$ over a field $K$ . With respect to Jimbo relations and the PBW $K$ -basis $B$ of $U_{q}^{+} (A_{N})$ (resp. $U_{q}^{-} (A_{N})$ ) established by Yamane, it is shown, by constructing an appropriate monomial ordering $≺$ on $B$ , that $U_{q}^{+} (A_{N})$ (resp. $U_{q}^{-} (A_{N})$ ) is a solvable polynomial algebra. Consequently, further structural properties of $U_{q}^{+} (A_{N})$ (resp. $U_{q}^{-} (A_{N})$ ) and their modules may be established and realized in a constructive-computational way.

13 pages

On The Algebras Uq±​(AN​): From A Constructive-Computational Viewpoint

Abstract

On The Algebras $U_{q}^{\pm} (A_{N})$ : From A Constructive-Computational Viewpoint