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Title: On stable categories of group algebras
Author: Poulton , Andrew
ISNI:       0000 0004 5351 8364
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2014
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We study the stable category of a group algebra AG over a regular ring A, for a finite group G. We construct a right adjoint to the inclusion of the stable subcategory of A-projective AG-modules into the full stable category. We use this functor to study the stable category of VG-lattices, where V is a complete discrete valuation ring. We focus on HelIer lattices, the kernels of projective covers of torsion OGmodules. If k is the residue field of 0, we show that the Heller lattices of the simple kG-modules generate a dense sub category of the stable category laU-OG of OG-lattices. Turning to more general kG-modules, we show that the stable endomorphism ring of the Heller lattice of a kG-module M is isomorphic to the trivial extension algebra of the stable endomorphism ring of M when 0 is ramified, generalising a result due to S. Kawata. We conclude by discussing the structure of a connected component of the stable AuslanderReiten quiver containing the Heller lattice of an indecomposable kG-module. We also give necessary and sufficient conditions for the middle term of the almost split sequence ending in a virtually irreducible lattice to be indecomposable
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available