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- W770041213 abstract "As announced in the introduction, in this last section we consider a particular kind of Rickard equivalences between blocks which, at least conjecturally, seems to be very frequent and which includes the case of the basic Morita equivalences discussed in Section 7. We keep all the notation of Section 18; in particular, M .. is an indecomposable D(G × G’)-module associated with b ⊗ (b’)°, which has projective restrictions to O(G× 1) and to O(1 × G’), P .. is a vertex of M .. and N .. is a DP ..-source of it, we set P = π(P ..) and P’ = π’(P ..), and we respectively denote by σ : P .. → P and σ’: P .. → P’ the group homomorphisms determined by π and π’. Assume that M .. defines a Rickard equivalence between b and b’: we say that this equivalence is basic if the DP .. -interior algebra End O (N) .. is Ker(σ)- and Ker(σ’)basic (cf. 13.2); that is to say, since the restrictions of N .. to Ker(σ) and to Ker(σ’) are both projective, this equivalence is basic if and only if, denoting by Δ(P ..) the diagonal subgroup of P .. × P .. and considering the action of P .. × P .. on the O-module End O (N ..) by left and right multiplication, End O (N) .. has (Ker(σ) x Ker(σ)) • Δ (P ..)- and (Ker(σ’) × Ker(σ’)) Δ(P ..)-stable O-bases." @default.
- W770041213 created "2016-06-24" @default.
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- W770041213 date "1999-01-01" @default.
- W770041213 modified "2023-09-30" @default.
- W770041213 title "Basic Rickard equivalences between Brauer blocks" @default.
- W770041213 doi "https://doi.org/10.1007/978-3-0348-8693-2_19" @default.
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