Une correspondance de modules pour les blocs à groupes de défaut abéliens

Abstract

Let b be a block of a finite group G with an abelian defect group P and an inertial quotient E. Let us denote by L the semi-direct product of P and E. If E is cyclic and acts freely on P−{1}, we prove that the stable categories of \(\mathcal{O}\)Gb- and \(\mathcal{O}\)L-modules are equivalent, as a consequence of a more general result, without any hypothesis on E, about partial covering exomorphisms relating \(\mathcal{O}\)Gb with a suitable twisted group algebra \(\mathcal{O}\)*\(\mathcal{O}\)