2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65754We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by h-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras.We construct a lift for any Lie quasi-bialgebra with zero cobracketQuantum Algebratext