2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153572Usually the generators of a quantum group are assumed to be commutative with the noncommuting coordinates of a quantum plane. We have relaxed the assumption and investigated its consequences. Not only does a two-parameter quantum group arise naturally, but also the formulation leads us to many probable quantum planes associated with a quantum group. Several examples are presented.Latex, 14 pages with no figureQuantum Algebratext