Extensions of Rickard equivalences

Rickard Equivalences and Block Theory

De nition We say that a subgroup H of G controls the fusion of p subgroups of G if the following two conditions are ful lled C H contains a Sylow p subgroup Sp of G C whenever P is a subgroup of Sp and g is an element of G such that gPg Sp there exist z in the centralizer CG P of P in G and h in H such that g hz Basic example We denote by Op G the largest normal subgroup of G with order prime t...

Block Theory via Stable and Rickard Equivalences

On graph equivalences preserved under extensions

Let G be the set of finite graphs whose vertices belong to some fixed countable set, and let ≡ be an equivalence relation on G. By the strengthening of ≡ we mean an equivalence relation ≡s such that G ≡s H , where G,H ∈ G, if for every F ∈ G, G ∪ F ≡ H ∪ F . The most important case that we study in this paper concerns equivalence relations defined by graph properties. We write G ≡ H , where Φ i...

Morita Equivalences Induced by Bimodules over Hopf-galois Extensions

Let H be a Hopf algebra, and A, B be H-Galois extensions. We investigate the category AM H B of relative Hopf bimodules, and the Morita equivalences between A and B induced by them. Introduction This paper is a contribution to the representation theory of Hopf-Galois extensions, as originated by Schneider in [15]. More specifically, we consider the following questions. Let H be a Hopf algebra, ...

Some Examples of Rickard Complexes

After a presentation of Brou e's conjecture for principal blocks with an abelian defect group, we describe a Rickard complex for GL 2 (q) arising from thè-adic cohomology of a Deligne-Lusztig variety, in accordance with the explicit form given by Brou e to his conjecture in the case of Chevalley groups in non natural characteristic.