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

Abstract

Let O be a complete discrete valuation ring, K its quotient field, and A the symmetric Kronecker algebra over O. We consider the full subcategory of the category of A-lattices whose objects are A-lattices M such that M⊗OK is projective A⊗OK-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.