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Eventually homological isomorphisms and Gorenstein projective modules

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We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.

singularity categoriesGorenstein defect categoriesGorenstein projective modulesAuslander-Reiten conjectureGorenstein symmetry conjectureeventually homological isomorphisms

Yongyun Qin、Dawei Shen

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School of Mathematics,Yunnan Normal University,Kunming 650500,China

School of Mathematics and Statistics,Henan University,Kaifeng 475004,China

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaScientific and Technological Planning Project of Yunnan ProvinceScientific and Technological Innovation Team of Yunnan Province

1206106011801141202305AC1600052020CXTD25

2024

10.1007/s11425-022-2146-5

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(8)
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