On Irreducible Morphisms and Auslander-Reiten Triangles in the Stable Category of Modules over Repetitive Algebras

Let be an algebraically closed field, let Λ be a finite dimensional -algebra, and let Λ be the repetitive algebra of Λ. For the stable category of finitely generated left Λ -modules Λ - mod , we prove that every Auslander-Reiten triangle in Λ - mod is induced from an Auslander-Reiten sequence of finitely generated left Λ -modules. We use this fact to show that the irreducible morphisms in Λ - mod fall into three canonical forms: (i) all the component morphisms are split monomorphisms; (ii) all of them are split epimorphisms; (iii) there is exactly one irreducible component. Finally, we use this classification to describe the shape of the Auslander-Reiten triangles in Λ - mod .