English

Auslander-Reiten Triangles in Homotopy Categories

Representation Theory 2015-12-01 v1

Abstract

Let AA be an artin algebra. We show that the bounded homotopy category of finitely generated right AA-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].

Keywords

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

R2 v1 2026-06-22T11:56:23.246Z