  For any Drinfeld-Jimbo quantum enveloping algebra Uq(g) and for any family
$\lambda =(\lambda \_{ij})\_{1\leq i < j\leq t} \in k^{\star}$ of invertible
elements of the base field, we explicitly construct a Galois object
$A\_{\lambda}$ 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 $A\_{\lambda}$.
