Perverse Equivalences and Broué's Conjecture

2010/10/07 by David Craven, David A. Craven, Raphaël Rouquier +2 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.1010.1378

50 pages

arxiv created 2010/10/07 · openalex publication_date 2010/10/07 · arxiv updated 2010/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new approach to the construction of derived equivalences between blocks of finite groups, based on perverse equivalences, in the setting of Broué's conjecture. We provide in particular local and global perversity data describing the principal blocks and the derived equivalences for a number of finite simple groups with Sylow subgroups C3xC3. We also examine extensions to automorphism groups in a general setting.

Cited by

• Broué's abelian defect group conjecture holds for the sporadic simple Conway group Co₃

Related

• An algorithmic approach to perverse derived equivalences: Broué's Conjecture for Ω⁺₈(2)
• Perverse Equivalences and Broué's Conjecture II: The Cyclic Case
• Splendid and perverse equivalences
• The Broué invariant of a p-permutation equivalence
• Broué's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group