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A trisection in the Auslander–Reiten quiver
Colloquium Mathematicum, 2022Let \(\Gamma\) 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, 1984The 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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A numerical characterization of finite Auslander-Reiten quivers
Lecture Notes in Mathematics, 1986Kiyoshi Igusa, Gordana Todorov
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Auslander-reiten quivers of schurian orders
Communications in Algebra, 1984We 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
2020Let 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, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hou, Bo, Yang, Shilin
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Semi-Stable Components of an Auslander-Reiten Quiver
Journal of the London Mathematical Society, 1993Let \(A\) 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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The Dual Quiver of the Auslander–Reiten Quiver of Path Algebras
Algebras and Representation Theory, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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