On the algebras : from a constructive-computational viewpoint

Abstract

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