Date Available
12-14-2011
Year of Publication
2009
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department
Mathematics
Advisor
Dr. Marian Anton
Co-Director of Graduate Studies
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
