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On a Generalized Auslander-Reiten Conjecture
It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric Auslander condition (SAC) are equivalent, and (GARC)...
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The stable Auslander-Reiten components of certain monomorphism categories
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...
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Relative tilting theory in abelian categories I: Auslander–Buchweitz–Reiten approximations theory in subcategories and cotorsion-like pairs
In this paper, we introduce a special kind of relative (co)resolutions associated with a pair of classes of objects in an abelian category
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Auslander–Reiten Triangles and Grothendieck Groups of Triangulated Categories
We prove that if the Auslander–Reiten triangles generate the relations for the Grothendieck group of a Hom-finite Krull–Schmidt triangulated category...
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The Simple Connectedness of Tame Algebras with Separating Almost Cyclic Coherent Auslander–Reiten Components
We study the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander–Reiten...
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The strong simple connectedness of tame algebras with separating almost cyclic coherent Auslander–Reiten components
We study the strong simple connectedness of finite-dimensional tame algebras over an algebraically closed field, for which the Auslander–Reiten...
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The Auslander–Reiten Formula on Finitely Presented Functor Categories
Let R be an artin algebra. The Auslander–Reiten formula for the category (mod- R )-mod of finitely presented functors is presented, which is extended...
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Auslander-Reiten Conjecture in a Dual Vein
We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian algebras over commutative Noetherian rings. Firstly, in the...
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Eventually homological isomorphisms and Gorenstein projective modules
We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity...
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Relative Auslander bijection in n-exangulated categories
The aim of this article is to study the relative Auslander bijection in n -exangulated categories. More precisely, we introduce the notion of...
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Shapes of Auslander-Reiten Triangles
Giraldo and Merklen classified the irreducible morphisms in the bounded derived categories of finite dimensional algebras in three classes. The...
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Tubes containing string modules in symmetric special multiserial algebras
Symmetric special multiserial algebras are algebras that correspond to decorated hypergraphs with orientation, called Brauer configurations. In this...
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Dessins D’Enfants, Brauer Graph Algebras and Galois Invariants
In this paper, we associate a finite dimensional algebra, called a Brauer graph algebra, to every clean dessin d’enfant by constructing a quiver...
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The Auslander–Reiten quiver of an algebra
Let A be a finite dimensional k-algebra. As seen in Corollary II.3.13 , every indecomposable A-module is the source, and the target, of an almost...
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∞-Tilting Subcategories in Extriangulated Categories
In this paper, the authors introduce a new definition of ∞-tilting (resp. cotilting) subcategories with infinite projective dimensions (resp....
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A geometric model for the module category of a skew-gentle algebra
In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked...
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Frobenius–Perron Theory of Representation-directed Algebras
We study the Frobenius–Perron dimension of representation-directed algebras and quotient algebras of canonical algebras of type ADE , prove that the...
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Serre Functors and Graded Categories
We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k -lin...