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}
}