Suppose R is a complete discrete valuation ring with exponential valuation v, G is a finite p-group. The representation type (finite, tame, or wild) of the group ring *L = RG had been determined in all cases but one; the case in which G = C3 and v(3)=4. The present book closes this gap. The author presents an explicit classification of all indecomposable lattices, as well as a description of the Auslander-Reiten quiver of *L, demonstrating that this is the only integral group ring whose representation type is non-domestic tame of finite growth. This book acquaints readers with various (by now classical) tame module categories, with techniques of matrix reduction, and with the interaction of basefree (category-theoretic) and base-dependent (matrix-theoretic) viewpoints and their respective relations to the combinatorial intuition provided by Auslander-Reiten quivers.
Table of contents:
Preliminaries: Notation and conventions; Generalized factorspace categories; Normal forms for local problems; Angular matrices and definition of subcategories; Dimension mappings; First reduction; Second reduction; Third reduction; Fourth reduction; The Auslander-Reiten quiver of *L; Appendix: Complete list of all indecomposable *L-lattices; The Auslander-Reiten quiver of M, Leitfaden.
Table of contents:
Preliminaries: Notation and conventions; Generalized factorspace categories; Normal forms for local problems; Angular matrices and definition of subcategories; Dimension mappings; First reduction; Second reduction; Third reduction; Fourth reduction; The Auslander-Reiten quiver of *L; Appendix: Complete list of all indecomposable *L-lattices; The Auslander-Reiten quiver of M, Leitfaden.