Shapes of Auslander-Reiten Triangles
  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. 
Edson Ribeiro Alvares, S\^onia Maria Fernandes, and Hern\'an Giraldo
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