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

Thomas Aubriot (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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 $A_{\lambda}$.

Mots clés: Noncommutative geometry; Principal fibre bundle; Galois extension; Hopf algebra; Drinfeld-Jimbo quantum group; Homotopy

Domaines: Algèbres quantiques [math.QA]

Thomas Aubriot. Classification of Galois objects of Uq(g) up to homotopy equivalence. Communication in Algebra, 2007, 35 (12), pp.3919--3936. ⟨10.1080/00927870701509446⟩. ⟨hal-00004479v3⟩