Rhetorical biset functors, rational \(p\)-biset functors and their semisimplicity in characteristic zero

DOI10.1016/J.JALGEBRA.2007.12.018zbMath1153.19001OpenAlexW2138820087MaRDI QIDQ933373

Laurence Barker

Publication date: 21 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.12.018

zbMATH Keywords

representation ringBurnside ringMackey functorbiset functorprimitive character.

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Modular representations and characters (20C20) Frobenius induction, Burnside and representation rings (19A22)

Related Items (21)

A ghost algebra of the double Burnside algebra in characteristic zero ⋮ Green fields ⋮ Tornehave morphisms. III: The reduced tornehave morphism and the Burnside unit functor. ⋮ The Roquette category of finite \(p\)-groups ⋮ Around evaluations of biset functors ⋮ Simple functors over the Green biset functor of section Burnside rings ⋮ Semisimplicity of some deformations of the subgroup category and the biset category ⋮ Simple modules over Green biset functors ⋮ Composition factors of functors ⋮ Essential support of Green biset functors via morphisms ⋮ A filtration of the modular representation functor ⋮ Alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules ⋮ On the ideals and essential algebras of shifted functors of linear representations ⋮ Obstructions for gluing biset functors ⋮ Inducing native Mackey functors to biset functors ⋮ Tornehave morphisms. II: The lifted Tornehave morphism and the dual of the Burnside functor ⋮ Rational \(p\)-biset functors ⋮ Quasi-hereditary property of double Burnside algebras ⋮ Tornehave Morphisms I: Resurrecting the Virtual Permutation Sets Annihilated by Linearization ⋮ Shifted functors of linear representations are semisimple ⋮ On the image of the trivial source ring in the ring of virtual characters of a finite group

Cites Work

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• Genotypes of irreducible representations of finite \(p\)-groups
• On the unit groups of Burnside rings
• Biset functors and genetic sections for \(p\)-groups
• The functor of rational representations for \(p\)-groups.
• Set functors equipped with a double action
• The functor of units of Burnside rings for \(p\)-groups
• Rational \(p\)-biset functors
• An induction theorem for the unit groups of Burnside rings of 2-groups
• The Dade group of a \(p\)-group.
• Detection theorems for K-theory and L-theory
• The Structure of Mackey Functors

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