Broué's conjecture for the hall-janko group and its double cover

• Autores: Miles Holloway
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 86, Nº 1, 2003, págs. 109-130
• Idioma: inglés
• DOI: 10.1112/s0024611502013795
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• Resumen

  • 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.