Diagonal \(p\)-permutation functors, semisimplicity, and functorial equivalence of blocks

DOI10.1016/j.aim.2022.108799OpenAlexW4309907970MaRDI QIDQ2105755

Deniz Yılmaz, Serge Bouc

Publication date: 8 December 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.12645

zbMATH Keywords

blocksemisimplediagonal \(p\)-permutation functorfunctorial equivalence

Mathematics Subject Classification ID

Modular representations and characters (20C20) Special categories (18B99) Category of groups (20J15)

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Cites Work

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• A ghost ring for the left-free double Burnside ring and an application to fusion systems
• Two classifications of simple Mackey functors with applications to group cohomology and the decomposition of classifying spaces
• Bisets as categories and tensor product of induced bimodules.
• Local methods in block theory
• Biset functors for finite groups
• The primitive idempotents of the \(p\)-permutation ring
• Local fusions in block source algebras
• A Frobenius theorem for blocks
• Pointed groups and construction of characters
• Simple modules over Green biset functors
• Fibered biset functors
• Shifted functors of linear representations are semisimple
• Diagonal \(p\)-permutation functors
• A General Approach to Green Functors Using Bisets
• ON THE NUMBER OF IRREDUCIBLE CHARACTERS OF FINITE GROUPS IN A GIVEN BLOCK
• On $p$-permutation equivalences: Between Rickard equivalences and isotypies
• On Scott Modules and p-Permutation Modules: An Approach through the Brauer Morphism
• The Block Theory of Finite Group Algebras
• Some deformations of the fibred biset category