Classifying blocks with abelian defect groups of rank 3 for the prime 2

JOURNAL OF ALGEBRA

卷:515

Article

Eaton, Charles¹  Livesey, Michael¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: Modular representation theory;    Block theory;    Morita equivalences;   

DOI  :  10.1016/j.jalgebra.2018.08.010

来源: Elsevier

【 摘 要 】

In this paper we classify all blocks with defect group C-2n x C-2 x C-2 up to Morita equivalence. Together with a recent paper of Wu, Zhang and Zhou, this completes the classification of Morita equivalence classes of 2-blocks with abelian defect groups of rank at most 3. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. The case considered in this paper is significant because it involves comparison of Morita equivalence classes between a group and a normal subgroup of index 2, so requires novel reduction techniques which we hope will be of wider interest. We note that this also completes the classification of blocks with abelian defect groups of order dividing 16 up to Morita equivalence. A consequence is that Broue's abelian defect group conjecture holds for all blocks mentioned above. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free