The A-fibered Burnside ring as A-fibered biset functor in\n characteristic zero

2019/09/14 by Robert Boltje, Deniz Yılmaz, Boltje, Robert +1 · 1 citation
Mathematics · #19A22 #20C15 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1909.06668

openalex publication_date 2019/09/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Let A be an abelian group such that \Hom(G,A) is finite for all\nfinite groups G, and let mathbbK be a field of characteristic zero\ncontaining roots of unity of all orders equal to finite element orders in A.\nIn this paper we prove foundational properties of the A-fibered Burnside ring\nfunctor B_ mathbbK^A as an A-fibered biset functor over mathbbK.\nThis includes the determination of the lattice of subfunctors of\nB_ mathbbK^A and the determination of the composition factors of\nB_ mathbbK^A. The results of the paper extend results of Co cskun and\nY i lmaz for the A-fibered Burnside ring functor restricted to p-groups and\nresults of Bouc in the case that A is trivial, i.e., the case of the Burnside\nring functor over fields of characteristic zero.\n

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• A Categorical Decomposition of \mathbb C^×-fibered p-biset Functors

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