Results 21 to 30 of about 2,837 (110)
On sectional paths in a category of complexes of fixed size [PDF]
, 2017 We show how to build the Auslander-Reiten quiver of the category Cn(proj A)of complexes of size n ≥ 2, for any artin algebra A. We also give conditions over the complexes in Cn(proj A) under which the composition of irreducible morphisms in sectional ...
Chaio, Claudia Alicia +2 more
core +2 more sources
Root Vectors Arising from Auslander–Reiten Quivers
Journal of Algebra, 1999 Let \(\mathfrak g\) be a semisimple Lie algebra, and \(U_q({\mathfrak g})\) its quantum enveloping algebra. Let \(\Lambda\) be the associated finite dimensional hereditary algebra over a finite field \(k\). In this paper the authors obtain a new algorithm to decompose the root vectors corresponding to preprojective and preinjective indecomposable ...
Chen, Xueqing, Xiao, Jie
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A characterization of finite Auslander—Reiten quivers
Journal of Algebra, 1984 Let \(\Gamma\) be a translation quiver with translation \(\tau\) [\textit{C. Riedtmann}, Comment. Math. Helv. 55, 199-224 (1980; Zbl 0444.16018)] and k a commutative field. A k-modulation on \(\Gamma\) consists of the following: (a) A finite dimensional division algebra \(F_ x\) over k for every vertex x of \(\Gamma\).
Igusa, Kiyoshi, Todorov, Gordana
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Jacobian algebras with periodic module category and exponential growth [PDF]
, 2015 The Jacobian algebra associated to a triangulation of a closed surface $S$ with a collection of marked points $M$ is (weakly) symmetric and tame. We show that for these algebras the Auslander-Reiten translate acts 2-periodical on objects.
Valdivieso-Díaz, Yadira
core +2 more sources
The Auslander-Reiten Components in the Rhombic Picture [PDF]
, 2012 For an indecomposable module $M$ over a path algebra of a quiver of type $\widetilde{\mathbb A}_n$, the Gabriel-Roiter measure gives rise to four new numerical invariants; we call them the multiplicity, and the initial, periodic and final parts.
Schmidmeier, Markus, Tyler, Helene R.
core +1 more source
Degrees of irreducible morphisms in generalized standard coherent almost cyclic components [PDF]
, 2017 We study the degrees of irreducible morphisms between indecomposablemodules lying in generalized standard coherent almost cyclic componentsof Auslander-Reiten quivers of artin algebras.Fil: Chaio, Claudia Alicia.
Chaio, Claudia Alicia, Malicki, Piotr
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Auslander algebras and initial seeds for cluster algebras [PDF]
, 2005 Let $Q$ be a Dynkin quiver and $\Pi$ the corresponding set of positive roots. For the preprojective algebra $\Lambda$ associated to $Q$ we produce a rigid $\Lambda$-module $I_Q$ with $r=|\Pi|$ pairwise non-isomorphic indecomposable direct summands by ...
Geiß, Christof +2 more
core +6 more sources
Algebraic modules and the Auslander–Reiten quiver
Journal of Pure and Applied Algebra, 2011 Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that non-periodic algebraic modules are very rare, and that if the complexity of an algebraic module is at least 3, then it is the only algebraic module ...
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Auslander-Reiten Components of Symmetric Special Biserial Algebras
, 2018 We provide a combinatorial algorithm for constructing the stable Auslander-Reiten component containing a given indecomposable module of a symmetric special biserial algebra using only information from its underlying Brauer graph.
Duffield, Drew
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Torsion classes of extended Dynkin quivers over commutative rings
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract For a Noetherian R$R$‐algebra Λ$\Lambda$, there is a canonical inclusion torsΛ→∏p∈SpecRtors(κ(p)Λ)$\mathop {\mathsf {tors}}\Lambda \rightarrow \prod _{\mathfrak {p}\in \operatorname{Spec}R}\mathop {\mathsf {tors}}(\kappa (\mathfrak {p})\Lambda)$, and each element in the image satisfies a certain compatibility condition.
Osamu Iyama, Yuta Kimura
wiley +1 more source