2015/11/29 by Yuefei Zheng, Zheng, Yuefei, Zhaoyong Huang +1
Mathematics · Physics and Astronomy · #16G10 #16G70 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1511.08964
openalex publication_date 2015/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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].