Classification of Galois objects of Uq(g) up to homotopy equivalence

Abstract

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 $A\_{\lambda}$.