Related papers: Finite and bounded Auslander-Reiten Components in …
We deduce a necessary condition for Auslander-Reiten components of the bounded derived category of a finite dimensional algebra to have Euclidean tree class by classifying certain types of irreducible maps in the category of complexes. This…
We provide criteria for an Auslander-Reiten component having sections of a Krull-Schmidt category to be standard. Specializing to the category of finitely presented representations of a strongly locally finite quiver and its bounded derived…
We show that if a connected, Hom-finite, Krull-Schmidt triangulated category has an Auslander-Reiten quiver component with Dynkin tree class then the category has Auslander-Reiten triangles and that component is the entire quiver. This is…
We classify the Auslander-Reiten components of the bounded derived category of \Lambda, where {\Lambda} is a cluster-tilted of type \~A. The main tool is the combinatoric description of the indecomposable complexes in the bounded homotopy…
Let $\Lambda$ be an Artin algebra and let $\rm{Gprj}\mbox{-}\Lambda$ denote the class of all finitely generated Gorenstein projective $\Lambda$-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a…
We study Auslander-Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-invertible maps between modules in the given component. First,…
Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. The main purpose of this paper is to get a better understanding of rep(Q) by means of…
We analyze Auslander-Reiten quivers of functorially finite resolving subcategories. Chapter 1 gives a short introduction into the basic definitions and theorems of Auslander-Reiten theory in A-mod. We generalize these definitions and…
We provide sufficient conditions for a component of the Auslander-Reiten quiver of an artin algebra to be determined by the composition factors of its indecomposable modules.
In this paper we show that the tree class of a component of the stable Auslander-Reiten quiver of a Frobenius-Lusztig kernel is one of the three infinite Dynkin diagrams. For the special case of the small quantum group we show that the…
This paper deals with the representation theory of a locally finite quiver in which the number of paths between any two given vertices is finite. We first study some properties of the finitely presented or co-presented representations, and…
We introduce a new combinatorial condition on a subinterval of a poset P (a clamped subinterval) that allows us to relate the Auslander-Reiten quiver of the bounded derived category of P to that of the subinterval. Applications include the…
Let $A$ be a truncated polynomial ring over a complete discrete valuation ring $\mathcal{O}$, and we consider the additive category consisting of $A$-lattices $M$ with the property that $M\otimes \mathcal{K}$ is projective as an $A\otimes…
We determine the structure of all finite-dimensional self-injective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice.
By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…
Our main theorem classifies the Auslander-Reiten triangles according to properties of the morphisms involved. As a consequence, we are able to compute the mapping cone of an irreducible morphism. We finish by showing a technique for…
Let $\mathbb{Z}$ be the integer numbers, $\mathbb{k}$ an algebraically closed field, $\Lambda$ a finite dimensional $\mathbb{k}$-algebra, mod$\Lambda$ the category of finitely generated right modules, proj$\Lambda$ the full subcategory of…
We provide a combinatorial algorithm for constructing the stable Auslander-Reiten component containing a given indecomposable module of a symmetric special biserial algebra using only information from its underlying Brauer graph. We also…
Peter Jorgensen introduced the Auslander-Reiten quiver of a simply connected Poincare duality space. He showed that its components are of the form ZA_infty and that the Auslander-Reiten quiver of a d-dimensional sphere consists of d-1 such…
The notion of an extriangulated category gives a unification of existing theories in exact or abelian categories and in triangulated categories. In this article, we develop Auslander--Reiten theory for extriangulated categories. This…