2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145670For any Drinfeld-Jimbo quantum enveloping algebra Uq(g) and for any family $λ=(λ\_{ij})\_{1\leq i < j\leq t} \in k^{\star}$ of invertible elements of the base field, we explicitly construct a Galois object $A\_λ$ of Uq(g) by generators and relations and we prove that any Galois object of Uq(g) is homotopic to a unique object of type $A\_λ$.To appear in Communications in Algebra. In FrenchQuantum Algebra16W30, 17B37, 55R10, 58B34, 81R50, 81R60text