Results 41 to 50 of about 2,837 (110)
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
wiley +1 more source
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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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
wiley +1 more source
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
wiley +1 more source
Derived categories of graded gentle one-cycle algebras
, 2017 Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules. This is applied
Kalck, Martin, Yang, Dong
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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
Universal deformation rings for the symmetric group S_4
, 2008 Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S_4 denote the symmetric group on 4 letters.
A. Wiles +18 more
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Combinatorial Auslander-Reiten quivers and reduced expressions
, 2015 In this paper, we introduce the notion of combinatorial Auslander-Reiten(AR) quiver for commutation classes $[\widetilde{w}]$ of $w$ in finite Weyl group. This combinatorial object visualizes the convex partial order $\prec_{[\widetilde{w}]}$ on the subset $Φ(w)$ of positive roots.
Oh, Se-Jin, Suh, Uhi Rinn
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