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 $\lambda =(\lambda \_ij)\_1\le i<j\le t\in k^{\star }$ 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 $A\_\lambda$.

arXiv commentTo appear in Communications in Algebra. In French