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The Auslander-Reiten quiver of a finite group

Mathematische Zeitschrift, 1982
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The Dual Quiver of the Auslander–Reiten Quiver of Path Algebras

Algebras and Representation Theory, 2010
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τ-Categories III: Auslander Orders and Auslander–Reiten Quivers

Algebras and Representation Theory, 2005
Important properties of Auslander orders over a complete discrete valuation domain are established in this paper. Roughly speaking, an Auslander order is an order \(\Lambda\) such that the category \(\text{pr\,}\Lambda\) of projective \(\Lambda\)-lattices is equivalent to a category of lattices over a (necessarily representation-finite) order.
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A trisection in the Auslander–Reiten quiver

Colloquium Mathematicum, 2022
Let \(\Gamma\) be an Artin algebra. Let \(\mathrm{ind}~\Gamma\) be the subcategory containing all isoclasses of indecomposable modules of \(\Gamma\). The article [\textit{D. Happel} et al., Tilting in abelian categories and quasitilted algebras. Providence, RI: American Mathematical Society (AMS) (1996; Zbl 0849.16011)] defined subcategories, denoted \(
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On Auslander-Reiten Quivers without Oriented Cycles

Bulletin of the London Mathematical Society, 1984
The covering techniques of \textit{K. Bongartz} and \textit{P. Gabriel} [see Invent. Math. 65, 331-378 (1982; Zbl 0482.16026)] reduce the study of the Auslander-Reiten quiver \(\Gamma_{\Lambda}\) of an algebra \(\Lambda\) of finite representation type to the universal cover \({\tilde \Gamma}{}_{\Lambda}\), i.e.
Larrión, F., Salmerón, L.
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Auslander-reiten quivers of schurian orders

Communications in Algebra, 1984
We shall consider orders ⋀ over a complete discrete rank one valuation ring R in a split full matrix ring containing a complete sex of primitive orthogonal idempot ents. In case s of finite lattice type and R is the power series ring in one variable over its residexe class field k , we give a description of its index composable lattices and its ...
K. W. Roggenkamp, A. Wiedemann
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The Auslander–Reiten quiver of an algebra

2020
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 split morphism, and thus fits into an almost split sequence. The knowledge of all almost split sequences implies the knowledge of all indecomposable A-modules, up to isomorphism, and all irreducible morphisms.
Ibrahim Assem, Flávio U. Coelho
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The duality of Auslander-Reiten quiver of path algebras

Czechoslovak Mathematical Journal, 2019
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Hou, Bo, Yang, Shilin
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Semi-Stable Components of an Auslander-Reiten Quiver

Journal of the London Mathematical Society, 1993
Let \(A\) be an Artin algebra and denote by \(\Gamma_ A\) the Auslander- Reiten quiver of \(A\) and by \(\tau\) the Auslander-Reiten translate. In this paper, the author investigates the shapes of the semi-stable components of \(\Gamma_ A\). A semi-stable component of \(\Gamma_ A\) is a connected component of the left stable part \({}_ l \Gamma_ A\) or
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Examples of Auslander–Reiten Quivers

2014
We have already pointed out in Sect.1.5 that Auslander–Reiten quivers provide a threefold information about the representation theory of the quiver, namely the indecomposable representations, the irreducible morphisms, and the almost split sequences—these in turn should be thought of the building blocks of arbitrary representations, morphisms, and ...
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