Real representation spheres and the real monomial Burnside ring
| Autor: | İpek Tuvay, Laurence Barker |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Pure mathematics Monomial Real representation spheres Functor Algebra and Number Theory Induced representation Mathematics::Commutative Algebra Burnside ring Quasi-finite morphism Monomial Lefschetz invariants Morphism Mathematics::Algebraic Geometry secondary 19A22 Mathematics::Category Theory primary 20C15 Real representation Invariant (mathematics) Real representations of finite groups Mathematics |
| Zdroj: | Journal of Algebra |
| Popis: | Cataloged from PDF version of article. We introduce a restriction morphism, called the Boltje morphism, from a given ordinary representation functor to a given monomial Burnside functor. In the case of a sufficiently large fibre group, this is Robert Boltje's splitting of the linearization morphism. By considering a monomial Lefschetz invariant associated with real representation spheres, we show that, in the case of the real representation ring and the fibre group {±1}, the image of a modulo 2 reduction of the Boltje morphism is contained in a group of units associated with the idempotents of the 2-local Burnside ring. We deduce a relation on the dimensions of the subgroup-fixed subspaces of a real representation. © 2011 Elsevier Inc. |
| Databáze: | OpenAIRE |
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