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University of Kentucky Doctoral Dissertations
Algebraic topology|Burnside ring|representation ring|elementary abelian p-group|cyclic p-group
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The Generalized Burnside And Representation Rings, Eric B. Kahn
The Generalized Burnside And Representation Rings, Eric B. Kahn
University of Kentucky Doctoral Dissertations
Making use of linear and homological algebra techniques we study the linearization map between the generalized Burnside and rational representation rings of a group G. For groups G and H, the generalized Burnside ring is the Grothendieck construction of the semiring of G × H-sets with a free H-action. The generalized representation ring is the Grothendieck construction of the semiring of rational G×H-modules that are free as rational H-modules. The canonical map between these two rings mapping the isomorphism class of a G-set X to the class of its permutation module …