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The stable Auslander-Reiten components of certain monomorphism categories

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Abstract

Let A be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category \({\cal{S}}(\text{Gprj-}\Lambda)\) containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category Gprj-Λ. In particular, for the finite components, we show that under certain mild conditions, their cardinalities are divisible by 3. We see that this three-periodicity phenomenon reoccurs several times in the paper.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 12101316). The authors thank the referees, whose many useful comments significantly improved the paper.

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  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Rasool Hafezi & Yi Zhang

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  1. Rasool Hafezi
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  2. Yi Zhang
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Correspondence to Rasool Hafezi.

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Hafezi, R., Zhang, Y. The stable Auslander-Reiten components of certain monomorphism categories. Sci. China Math. 67, 505–526 (2024). https://doi.org/10.1007/s11425-022-2095-1

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