On periodic stable Auslander-Reiten components containing Heller lattices over the symmetric Kronecker algebra

Abstract

Let $\mathcal{O}$ be a complete discrete valuation ring, $\mathcal{K}$ its quotient field, and let $A$ be the symmetric Kronecker algebra over $\mathcal{O}$. We consider the full subcategory of the category of $A$-lattices whose objects are $A$-lattices $M$ such that $M\otimes_{\mathcal{O}}\mathcal{K}$ is projective $A\otimes_{\mathcal{O}}\mathcal{K}$-modules. In this paper, we study Heller lattices of indecomposable periodic modules over the symmetric Kronecker algebra. As a main result, we determine the shapes of stable Auslander-Reiten components containing Heller lattices of indecomposable periodic modules over the symmetric Kronecker algebra.Comment: 35 pages (v1), correct several errors (v2