2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55730We construct quantum deformations of the integrals of motion of the generalized mKdV equations for $\hat {\SL}_2$. For this, we give the relevant vertex operator algebra and prove quantum Serre relations for vertex operators, it allows to construct a $q$-BGG resolution and to deform the classical integrals of motion in a commutativ family.22 pages, LaTex, no figureHigh Energy Physics - TheoryExactly Solvable and Integrable Systemstext