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arXiv · 1511.08964

Auslander-Reiten Triangles in Homotopy Categories

Yuefei Zheng·Zhaoyong Huang
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Abstract

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

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Yuefei Zheng, Zhaoyong Huang. 2015-11-29. Auslander-Reiten Triangles in Homotopy Categories. https://arxiv.org/abs/1511.08964

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