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Broué's Conjecture for the Hall–Janko Group and its Double Cover
Author(s) -
Holloway Miles
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013795
Subject(s) - mathematics , conjecture , abelian group , cover (algebra) , equivalence (formal languages) , block (permutation group theory) , group (periodic table) , combinatorics , pure mathematics , covering space , algebra over a field , physics , quantum mechanics , mechanical engineering , engineering
Broué's abelian defect conjecture suggests a deep link between the module categories of a block of a group algebra and its Brauer correspondent, viz. that they should be derived equivalent. We are able to verify Broué's conjecture for the Hall–Janko group, even its double cover 2. J 2 , as well as for U 3 (4) and Sp 4 (4). In fact we verify Rickard's refinement to Broué's conjecture and show that the derived equivalence can be chosen to be a splendid equivalence for these examples. 2000 Mathematical Subject Classification: 20C20, 20C34.