Splendid and perverse-equivalences

JOURNAL OF ALGEBRA

卷:450

Article

Dreyfus-Schmidt, Leo¹ 

[1] Univ Paris Denis Diderot, Inst Math Jussieu Paris Rive Gauche, Batiment Sophie Germain, F-75205 Paris 13, France

关键词: Representation theory of finite groups;    Derived equivalences;    Splendid equivalences;    Perverse equivalences;   

DOI  :  10.1016/j.jalgebra.2015.10.018

来源: Elsevier

【 摘 要 】

Inspired by the works of Rickard on splendid equivalences [9] and of Chuang and Rouquier on perverse equivalences (6], we are here interested in the combination of both, i.e. a splendid perverse equivalence. This is naturally the right framework to understand the relations between global and local perverse equivalences between blocks of finite groups, as a splendid equivalence induces local derived equivalences via the Brauer functor. We prove that under certain conditions, we have an equivalence between a perverse equivalence between the homotopy category of p-permutation modules and local derived perverse equivalences, in the case of abelian defect groups. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free