Results 61 to 70 of about 2,140 (101)

Introduction to τ-tilting theory. [PDF]

Proc Natl Acad Sci U S A, 2014
Iyama O, Reiten I.
europepmc   +1 more source

Cluster algebras. [PDF]

Proc Natl Acad Sci U S A, 2014
Leclerc B, Williams LK.
europepmc   +1 more source

The Auslander-Reiten quiver of the category of m−periodic complexes

Journal of Pure and Applied Algebra
Let $\mathcal{A}$ be an additive $k-$category and $\mathbf{C}_{\equiv m}(\mathcal{A})$ be the category of $m-$periodic objects. For any integer $m>1$, we study conditions under which the compression functor ${\mathcal F}_m :\mathbf{C}^{b}(\mathcal{A}) \rightarrow \mathbf{C}_{\equiv m}(\mathcal{A})$ preserves or reflects irreducible morphisms ...
Claudia Chaio, Alfredo González Chaio, Isabel Pratti, María José Souto Salorio   +3 more
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A categorification of combinatorial Auslander-Reiten quivers

We provide a categorification of Oh and Suh's combinatorial Auslander-Reiten quivers in the simply laced case. We work within the perfectly valued derived category $\mathrm{pvd}(Π_Q)$ of the 2-dimensional Ginzburg dg algebra of a Dynkin quiver $Q$. For any commutation class $[i]$ of reduced words in the corresponding Weyl group, we define a subcategory
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Mesh-comparable components of the Auslander-Reiten quiver

The idea of using Riedtmann's well-behaved functors to study compositions of irreducible morphisms has been explored in a number of articles. Here we introduce the concept of mesh-comparable components of the Auslander-Reiten quiver, which are components for which a Riedtmann functor exists without the necessity of taking a covering, such as the ...
Chust, Viktor, Coelho, Flávio U.
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Additive og subadditive funksjoner og Auslander-Reiten-quiver

, 2016
I denne oppgaven studerer vi Cartanmatriser, additive og subadditive funksjoner og translasjonsquivre. Spesielt vil vi se hvordan additive og subadditive funksjoner er definert både for Cartanmatriser og for translasjonsquivre, og hvordan disse funksjonene gir restriksjoner for Cartanklassen til et stabilt valuert sammenhengende translasjonsquiver som ...
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The Auslander-Reiten quiver of a finite group

Mathematische Zeitschrift, 1982
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Examples of Auslander–Reiten Quivers

CMS Books in Mathematics, 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 ...
Ralf Schiffler
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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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Lie algebras determined by finite auslander-reiten quivers

Communications in Algebra, 1998
(1998). Lie algebras determined by finite auslander-reiten quivers. Communications in Algebra: Vol. 26, No. 9, pp. 2711-2725.
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