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

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