Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-16T15:52:49.501Z Has data issue: false hasContentIssue false
  • English
  • Français

BROUÉ'S CONJECTURE FOR THE HALL–JANKO GROUP AND ITS DOUBLE COVER

Published online by Cambridge University Press:  28 January 2003

MILES HOLLOWAY
MILES HOLLOWAY
Affiliation:
University of Oxford, The Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB. holloway@maths.ox.ac.uk
Get access

Abstract

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 ${\rm Sp}_4(4)$. 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.

Keywords

Broué's conjecturederived equivalenceHall–Janko group
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 86 , Issue 1 , January 2003 , pp. 109 - 130
Copyright
2003 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)