Results 1 to 10 of about 2,140 (101)
Auslander?Reiten Quivers and the Coxeter Complex [PDF]
Algebras and Representation Theory, 2005 Let Q be a quiver of type ADE. We construct the corresponding Auslander-Reiten quiver as a topological complex inside the Coxeter complex associated with the underlying Dynkin diagram. We use the notion of chamber weights coming from the theory of the canonical basis of quantized envelopping algebras, and show this set has a special linearity property ...
Shmuel Zelikson
exaly +6 more sources
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 \(\Gamma\).
Kiyoshi Igusa
exaly +3 more sources
The Auslander–Reiten Quiver of a Poincaré Duality Space
Algebras and Representation Theory, 2006 In a previous paper, math.AT/0304079, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincare duality space, each component of the Auslander-Reiten quiver is isomorphic to ZA_{\infty}.
exaly +4 more sources
Components of Auslander-Reiten Quivers with Only Preprojective Modules
Journal of Algebra, 1993 If \(A\) is an Artin algebra, a connected component \({\mathcal C}\) of its Auslander-Reiten quiver \(\Gamma_ A\) is a \(\pi\)-component if all indecomposables in \({\mathcal C}\) are preprojective in the sense of \textit{M. Auslander} and \textit{S. O. Samlø} [see J. Algebra 66, 61-122 (1980; Zbl 0477.16013)].
exaly +3 more sources
Auslander-Reiten quivers of local, orders of finite lattice type
Manuscripta Mathematica, 1987 Let R be a complete d.v.r. with quotient field K and \(\Lambda\) a representation-finite local R-order in a semisimple K-algebra A. The classification of Auslander-Reiten quivers \({\mathcal A}(\Lambda)\) of such \(\Lambda\) is completed in this paper. Previously, the author classified \({\mathcal A}(\Lambda)\) for \(\Lambda\) Gorenstein, while \textit{
exaly +2 more sources
Persistence Modules on Commutative Ladders of Finite Type [PDF]
, 2015 We study persistence modules defined on commutative ladders. This class of persistence modules frequently appears in topological data analysis, and the theory and algorithm proposed in this paper can be applied to these practical problems.
Escolar, Emerson G., Hiraoka, Yasuaki
core +1 more source
Coxeter elements and periodic Auslander–Reiten quiver
Journal of Algebra, 2010 27 pages, 10 figures.
Kirillov, A., Thind, J.
openaire +3 more sources
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
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On Auslander-Reiten components of algebras without external short paths [PDF]
, 2011 We describe the structure of semi-regular Auslander-Reiten components of artin algebras without external short paths in the module category. As an application we give a complete description of self-injective artin algebras whose Auslander-Reiten quiver ...
Jaworska, Alicja +2 more
core +4 more sources
Degrees of irreducible morphisms and finite-representation type [PDF]
, 2009 We study the degree of irreducible morphisms in any Auslander-Reiten component of a finite dimensional algebra over an algebraically closed field. We give a characterization for an irreducible morphism to have finite left (or right) degree.
Chaio, Claudia +2 more
core +4 more sources