Results 1 to 10 of about 331 (40)
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras [PDF]
Open Mathematics, 2014 We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by ...
Malicki Piotr +2 more
doaj +3 more sources
The symplectic geometry of higher Auslander algebras: Symmetric products of disks
Forum of Mathematics, Sigma, 2021 We show that the perfect derived categories of Iyama’s d-dimensional Auslander algebras of type ${\mathbb {A}}$ are equivalent to the partially wrapped Fukaya categories of the d-fold symmetric product of the $2$-dimensional unit disk with finitely many ...
Tobias Dyckerhoff +2 more
doaj +1 more source
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 bijections and universal extensions [PDF]
, 2017 Universal extensions arise naturally in the Auslander bijections. For an abelian category having Auslander-Reiten duality, we exploit a bijection triangle, which involves the Auslander bijections, universal extensions and the Auslander-Reiten duality ...
Chen, Xiao-Wu
core +1 more source
Reconstruction algebras of type D (II) [PDF]
, 2013 This is the third in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin quivers.
Wemyss, Michael
core +1 more source
Cluster tilting vs. weak cluster tilting in Dynkin type A infinity [PDF]
, 2014 This paper shows a new phenomenon in higher cluster tilting theory. For each positive integer d, we exhibit a triangulated category C with the following properties.
Holm, Thorsten, Jorgensen, Peter
core +4 more sources
Auslander-Reiten triangles and Grothendieck groups of triangulated categories
, 2021 We prove that if the Auslander-Reiten triangles generate the relations for the Grothendieck group of a Hom-finite Krull-Schmidt triangulated category with a (co)generator, then the category has only finitely many isomorphism classes of indecomposable ...
Haugland, Johanne
core
, 2019 These notes are an expanded version of my talk at the ICRA 2018 in Prague, Czech Republic; they are based on joint work with Tobias Dyckerhoff and Tashi Walde.
Jasso, Gustavo
core +1 more source
, 2015 Given a finite acyclic quiver Q with path algebra kQ, Ingalls and Thomas have exhibited a bijection between the set of Morita equivalence classes of support-tilting modules and the set of thick subcategories of mod kQ and they have collected a large ...
Fakieh, Wafaa M. +3 more
core +1 more source
Gabriel-Roiter inclusions and Auslander-Reiten theory
, 2009 Let $\Lambda$ be an artin algebra. The aim of this paper is to outline a strong relationship between the Gabriel-Roiter inclusions and the Auslander-Reiten theory. If $X$ is a Gabriel-Roiter submodule of $Y,$ then $Y$ is shown to be a factor module of an
Ringel, Claus Michael
core +1 more source