Results 41 to 50 of about 2,140 (101)
Cluster categories for completed infinity‐gons I: Categorifying triangulations
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity‐gons, which are discs with an infinite closed set of marked points on their boundary. These categories have many features in common with the cluster categories associated to discs with different sets of marked points. In particular, they have (weak)
İlke Çanakçı +2 more
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Harder–Narasimhan filtrations of persistence modules
Transactions of the London Mathematical Society, Volume 11, Issue 1, December 2024.Abstract The Harder–Narasimhan (HN) type of a quiver representation is a discrete invariant parameterised by a real‐valued function (called a central charge) defined on the vertices of the quiver. In this paper, we investigate the strength and limitations of HN types for several families of quiver representations which arise in the study of persistence
Marc Fersztand +3 more
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Semistable torsion classes and canonical decompositions in Grothendieck groups
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract We study two classes of torsion classes that generalize functorially finite torsion classes, that is, semistable torsion classes and morphism torsion classes. Semistable torsion classes are parametrized by the elements in the real Grothendieck group up to TF equivalence.
Sota Asai, Osamu Iyama
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, 2007 We show that an algebraic 2-Calabi-Yau triangulated category over an algebraically closed field is a cluster category if it contains a cluster tilting subcategory whose quiver has no oriented cycles. We prove a similar characterization for higher cluster
Keller, Bernhard, Reiten, Idun
core +1 more source
Almost Cyclic Coherent Components of an Auslander–Reiten Quiver
Journal of Algebra, 2000 The authors study very closely the cyclic part \(_c\Gamma_A\) of the A-R quiver of an Artin algebra \(A\). The definition of the quiver \(_c\Gamma_A\) is the following: A vertex \(X\) of the A-R quiver is called cyclic if it lies on an oriented cycle of \(\Gamma_A\).
Malicki, Piotr, Skowroński, Andrzej
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Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.Abstract We define a class of associative algebras generalizing ‘clannish algebras’, as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well‐known ‘string algebras’ introduced by Butler and Ringel.
Raphael Bennett‐Tennenhaus +1 more
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On Specht Modules in the Auslander-Reiten Quiver
Journal of Algebra, 1995 Let \(\Lambda\) be a finite-dimensional algebra over a field \(F\). The Auslander-Reiten quiver (AR quiver) \(\Gamma(\Lambda)\) of \(\Lambda\), a certain directed graph on the isomorphism classes of indecomposable \(\Lambda\)-modules, is an important homological invariant of the algebra, and it has been of major use for studying representations.
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A functorial approach to monomorphism categories II: Indecomposables
Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.Abstract We investigate the (separated) monomorphism category mono(Q,Λ)$\operatorname{mono}(Q,\Lambda)$ of a quiver over an Artin algebra Λ$\Lambda$. We show that there exists an epivalence (called representation equivalence in the terminology of Auslander) from mono¯(Q,Λ)$\overline{\operatorname{mono}}(Q,\Lambda)$ to rep(Q,mod¯Λ)$\operatorname{rep}(Q,\
Nan Gao +3 more
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Infinitesimal semi‐invariant pictures and co‐amalgamation
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract The purpose of this paper is to study the local structure of the semi‐invariant picture of a tame hereditary algebra near the null root. Using a construction that we call co‐amalgamation, we show that this local structure is completely described by the semi‐invariant pictures of a collection of self‐injective Nakayama algebras.
Eric J. Hanson +3 more
wiley +1 more source
A characterization of admissible algebras with formal two-ray modules
, 2005 In the paper we characterize, in terms of quivers and relations, the admissible algebras with formal two-ray modules introduced by G. Bobi\'nski and A. Skowro\'nski [Cent. Eur. J.Math.1 (2003), 457--476].Comment: Mainly correcting typos.
Drozd Yu. A. +5 more
core +3 more sources