2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187236In this paper,we derive a $\hbar$-deformation of the $W_{N}$ algebra and its quantum Miura tranformation. The vertex operators for this $\hbar$-deformed $W_{N}$ algebra and its commutation relations are also obtained.16 pagesHigh Energy Physics - TheoryA $\hbar$-deformation of the $W_{N}$ algebra and its vertex operatorstext