Un scindage du morphisme de Frobenius quantique

Michel Gros (1) , Masaharu Kaneda (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics

We show that the quantum Frobenius morphism constructed by Lusztig in the setting of the quantum enveloping algebra specialized at a root of unity admits a multiplicative splitting (non unital). We also find a basis of the toral part of the small quantum algebra consisting of pairwise orthogonal idempotents summing up to 1, and likewise in the modular case of the algebra of distributions for a semisimple algebraic group.

Domaines: Théorie des représentations [math.RT]; Algèbres quantiques [math.QA]

Michel Gros, Masaharu Kaneda. Un scindage du morphisme de Frobenius quantique. Arkiv för Matematik, 2015, 53 (2), pp.271-301. ⟨10.1007/s11512-014-0205-8⟩. ⟨hal-00833303⟩