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The stable Auslander-Reiten components of certain monomorphism categories

Science China Mathematics 2024年第3期67卷 505-526页

作者： rasool hafezi Yi Zhang School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China

Let Λ 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 S(Gprj-Λ) 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. 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.

关键词： monomorphism category almost split sequence Auslander-Reiten quiver Gorenstein projective module

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On the monomorphism category of n-cluster tilting subcategories

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Science China Mathematics 2022年第7期65卷 1343-1362页

作者： Javad Asadollahi rasool hafezi Somayeh Sadeghi Department of Pure Mathematics Faculty of Mathematics and StatisticsUniversity of IsfahanIsfahan 81746-73441Iran School of Mathematics and Statistics Nanjing University of Information Science&TechnologyNanjing 210044China

Let M be an n-cluster tilting subcategory of mod-Λ,whereΛis an Artin *** S(M)denote the full subcategory of S(Λ),the submodule category of Λ,consisting of all the monomorphisms in *** construct two functors from S(M)to mod-Λ,the category of finitely presented additive contravariant functors on the stable category of *** show that these functors are full,dense and objective and hence provide equivalences between the quotient categories of S(M)and mod-Λ.We also compare these two functors and show that they differ by the n-th syzygy functor,provided M is an n Z-cluster tilting *** functors can be considered as higher versions of the two functors studied by Ringel and Zhang(2014)in the case Λ=k[x]/and generalized later by Eiríksson(2017)to self-injective Artin *** applications are provided.

关键词： submodule categories n-abelian categories n-cluster tilting subcategories

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A functorial approach to categorical resolutions

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Science China Mathematics 2020年第10期63卷 2005-2016页

作者： rasool hafezi Mohammad Hossein Keshavarz School of Mathematics Institute for Research in Fundamental Sciences(IPM)Tehran 19395-5746Iran

Using a relative version of Auslander’s formula,we give a functorial approach to show that the bounded derived category of every Artin algebra admits a categorical ***,in particular,implies that the bounded derived categories of Artin algebras of finite global dimension determine bounded derived categories of all Artin ***,this paper can be considered as a typical application of functor categories,introduced in representation theory by Auslander(1971),to categorical resolutions.

关键词： categorical resolutions Artin algebras Auslander’s formula

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