Equivalences between blocks of p-local Mackey algebras

JOURNAL OF ALGEBRA

卷:428

Article

Rognerud, Baptiste

关键词: Modular representation;    Finite group;    Mackey functor;    Block theory;   

DOI  :  10.1016/j.jalgebra.2015.01.013

来源: Elsevier

【 摘 要 】

Let G be a finite group and (K, O, k) be a p-modular system. Let R = O or k. There is a bijection between the blocks of the group algebra and the blocks of the so-called p-local Mackey algebra mu(1)(R)(G). Let b be a block of RG with abelian defect group D. Let b' be its Brauer correspondant in N-G(D). It is conjectured by Broue that the blocks RGb and RNG(D)b' are derived equivalent. Here we look at equivalences between the corresponding blocks of p-local Mackey algebras. We prove that an analogue of the Broue's conjecture is true for the p-local Mackey algebras in the following cases: for the principal blocks of p-nilpotent groups and for blocks with defect 1. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free