Green correspondence on centric Mackey functors over fusion systems

DOI10.1016/J.JALGEBRA.2023.09.041zbMath1530.20044arXiv2208.07125OpenAlexW4387520096MaRDI QIDQ6066484

Marco Praderio Bova

Publication date: 16 November 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.07125

zbMATH Keywords

Green correspondencefusion systemsMackey functors

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Modular representations and characters (20C20) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15) Frobenius induction, Burnside and representation rings (19A22) Category of groups (20J15)

Cites Work

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• Two classifications of simple Mackey functors with applications to group cohomology and the decomposition of classifying spaces
• Mackey functors and bisets.
• Transfer and characteristic idempotents for saturated fusion systems
• Biset functors for finite groups
• The Burnside ring of fusion systems
• Green correspondence and transfer theorems of Wielandt type for G- functors
• Homotopy decomposition of classifying spaces via elementary Abelian subgroups
• The classification of \(p\)-local finite groups over the extraspecial group of order \(p^3\) and exponent \(p\).
• Fused Mackey functors
• A transfer theorem for modular representations
• Frobenius categories.
• Axiomatic representation threory for finite groups
• The Structure of Mackey Functors
• Subgroup families controlling p-local finite groups

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