Auslander–Reiten Triangles in Homotopy Categories.

LetAbe an artin algebra. We show that the bounded homotopy category of finitely generated rightA-modules has Auslander–Reiten triangles. Two applications are given: (1) we provide an alternative proof of a theorem of Happel in [14]; (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 improve a main result in [12]. [ABSTRACT FROM PUBLISHER]