Auslander-Reiten Triangles in Homotopy Categories
Representation Theory
2015-12-01 v1
Abstract
Let be an artin algebra. We show that the bounded homotopy category of finitely generated right -modules has Auslander-Reiten triangles. Two applications are given: (1) we provide an alternative proof of a theorem of Happel in [H2]; (2) we prove that over a Gorenstein algebra, the bounded homotopy category of finitely generated Gorenstein projective (resp. injective) modules admits Auslander-Reiten triangles, which improves a main result in [G].
Cite
@article{arxiv.1511.08964,
title = {Auslander-Reiten Triangles in Homotopy Categories},
author = {Yuefei Zheng and Zhaoyong Huang},
journal= {arXiv preprint arXiv:1511.08964},
year = {2015}
}
Comments
10 pages, accepted for publication in Communications in Algebra