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Shapes of Auslander-Reiten Triangles

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arxiv 1610.08457 v1 pith:Q6Q2HJUO submitted 2016-10-26 math.RT

Edson Ribeiro Alvares , Sônia Maria Fernandes , Hernán Giraldo This is my paper · ORCID
classification math.RT
keywords algebraauslander-reitencategoryconstructingderivedtechniquetiltedtriangles
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Our main theorem classifies the Auslander-Reiten triangles according to properties of the morphisms involved. As a consequence, we are able to compute the mapping cone of an irreducible morphism. We finish by showing a technique for constructing the connecting component of the derived category of any tilted algebra. In particular we obtain a technique for constructing the derived category of any tilted algebra of finite representation type.

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  1. On irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over repetitive algebras

    math.RT 2019-08 accept novelty 5.0 of 10

    Irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over a repetitive algebra take three canonical shapes, and every such triangle is induced by an Auslander-Reiten sequence.

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