2019/08/08 by Calderón-Henao, Yohny, Giraldo, Hernán, Vélez-Marulanda, José A.
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1908.02912
Let k be an algebraically closed field, let Λ be a finite dimensional k-algebra, and let \widehatΛ be the repetitive algebra of Λ. For the stable category of finitely generated left \widehatΛ-modules \widehatΛ-\underlinemod, we show that the irreducible morphisms 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. We next use this fact in order to describe the shape of the Auslander-Reiten triangles in \widehatΛ-\underlinemod. We use the fact (and prove) that every Auslander-Reiten triangle in \widehatΛ-\underlinemod is induced from an Auslander-Reiten sequence of finitely generated left \widehatΛ-modules.