Morita equivalence classes of 2-blocks with abelian defect groups of rank 4

被引：2
作者：
Eaton, Charles W. [1 ]
Livesey, Michael [1 ]
机构：
[1] Univ Manchester, Dept Math, Manchester M13 9PL, England
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2024年 / 109卷 / 06期
基金：
英国工程与自然科学研究理事会;
关键词：
NILPOTENT BLOCKS; CONJECTURE; ALGEBRAS; EXTENSIONS;
D O I：
10.1112/jlms.12943
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We classify all 2-blocks with abelian defect groups of rank 4 up to Morita equivalence. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. An application is that Brou & eacute;'s abelian defect group conjecture holds for all blocks under consideration here.
引用
收藏
页数：26
相关论文
共 56 条
[1]   LOCAL METHODS IN BLOCK THEORY [J].
ALPERIN, J ;
BROUE, M .
ANNALS OF MATHEMATICS, 1979, 110 (01) :143-157
[2]  
An JB, 2023, Arxiv, DOI arXiv:2310.02150
[3]   Broue's Conjecture for 2-Blocks with Elementary Abelian Defect Groups of Order 32 [J].
Ardito, Cesare Giulio ;
Sambale, Benjamin .
ADVANCES IN GROUP THEORY AND APPLICATIONS, 2021, 12 :71-78
[4]   MORITA EQUIVALENCE CLASSES OF PRINCIPAL BLOCKS WITH ELEMENTARY ABELIAN DEFECT GROUPS OF ORDER 64 [J].
Ardito, Cesare Giulio .
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2021, 27 (01) :220-239
[5]   Morita equivalence classes of blocks with elementary abelian defect groups of order 32 [J].
Ardito, Cesare Giulio .
JOURNAL OF ALGEBRA, 2021, 573 :297-335
[6]  
Aschbacher M., 1986, Finite Group Theory, Cambridge Studies in Advanced Mathematics, V10
[7]  
Aschbacher M., 2011, Fusion systems in algebra and topolgy, V391
[8]  
Benson D.J., 1991, REPRESENTATIONS COHO, V30
[9]  
BESSENRODT C, 1989, J LOND MATH SOC, V39, P61
[10]   On Picard groups of blocks of finite groups [J].
Boltje, Robert ;
Kessar, Radha ;
Linckelmann, Markus .
JOURNAL OF ALGEBRA, 2020, 558 :70-101
123456