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- W2965517797 abstract "Let $mathbf{k}$ be an algebraically closed field, let $Lambda$ be a finite dimensional $mathbf{k}$-algebra, and let $widehat{Lambda}$ be the repetitive algebra of $Lambda$. For the stable category of finitely generated left $widehat{Lambda}$-modules $widehat{Lambda}$-underline{mod}, 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 $widehat{Lambda}$-underline{mod}. We use the fact (and prove) that every Auslander-Reiten triangle in $widehat{Lambda}$-underline{mod} is induced from an Auslander-Reiten sequence of finitely generated left $widehat{Lambda}$-modules." @default.
- W2965517797 created "2019-08-13" @default.
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- W2965517797 date "2019-08-08" @default.
- W2965517797 modified "2023-10-16" @default.
- W2965517797 title "On irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over repetitive algebras" @default.
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