English

Shapes of Auslander-Reiten Triangles

Representation Theory 2016-10-27 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1610.08457,
  title  = {Shapes of Auslander-Reiten Triangles},
  author = {Edson Ribeiro Alvares and Sônia Maria Fernandes and Hernán Giraldo},
  journal= {arXiv preprint arXiv:1610.08457},
  year   = {2016}
}