2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152603An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all principle W-algebras associated with the simple Lie algebras. The proof is based on the more general result that for a class of vertex operators the quantum operators are related to their classical counterparts by an equivalence transformation.22 pages, 2 fig. includedHigh Energy Physics - TheoryQuantum Algebratext