ON THE NON-PERIODIC STABLE AUSLANDER-REITEN HELLER COMPONENT FOR THE KRONECKER ALGEBRA OVER A COMPLETE DISCRETE VALUATION RING

摘要

We consider the Kronecker algebra A =O[X, Y]/(X-2, Y-2), where O is a complete discrete valuation ring. Since A circle times k is a special biserial algebra, where kappa is the residue field of O, one can compute a complete list of indecomposable A circle times k modules. For each indecomposable A circle times k-module, we obtain a special kind of A-lattices called "Heller lattices". In this paper, we determine the non-periodic component of a variant of the stable Auslander-Reiten quiver for the category of A-lattices that contains "Heller lattices".