2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149540The relations between $L^{\pm}$ operators and the generators in the quantum enveloping algebras are studied. The $L^{\pm}$ operators for $U_{q}A_{N}$ and $U_{q}G_{2}$ algebras are explicitly expressed by the generators as examples.11 pages, no figure, LatexQuantum Algebratext