Date Available
12-14-2011
Year of Publication
2009
Degree Name
Doctor of Philosophy (PhD)
Document Type
Dissertation
College
Arts and Sciences
Department
Mathematics
First Advisor
Dr. Marian Anton
Second Advisor
Dr. Edgar Enochs
Abstract
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 is known as the linearization map. For p a prime number and H the unique group of order p, we describe the generators of the kernel of this map in the cases where G is an elementary abelian p-group or a cyclic p-group. In addition we introduce the methods needed to study the Bredon homology theory of a G-CW-complex with coefficients coming from the classical Burnside ring.
Recommended Citation
Kahn, Eric B., "THE GENERALIZED BURNSIDE AND REPRESENTATION RINGS" (2009). University of Kentucky Doctoral Dissertations. 707.
https://uknowledge.uky.edu/gradschool_diss/707
