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 $A$ 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 $A$. As a main result, we determine the shapes of stable Auslander--Reiten components containing Heller lattices of indecomposable periodic modules over $A$.

arXiv comment35 pages (v1), correct several errors (v2), correct several errors (v3), correct some typos (v4)