On selfinjective algebras without short cycles in the component quiver
We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
On selfinjective artin algebras having nonperiodic generalized standard Auslander-Reiten components
We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
On the existence of almost split sequences in subcategories
On the genus of the graph of tilting modules.
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
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 5.
On the numbers of discrete indecomposable modules over tame algebras
On the Represantation Theory of Artinian Rings and Artins Problems on Division Ring Extensions
On the structure of Calabi-Yau categories with a cluster tilting subcategory.
On the structure of triangulated categories with finitely many indecomposables
We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field . We obtain a new proof of the following result due to Xiao and Zhu: the Auslander-Reiten quiver of such a category is of the form where is a disjoint union of simply-laced Dynkin diagrams and a weakly admissible group of automorphisms of . Then we prove that for ‘most’ groups , the category is standard,i.e.-linearly...
On the trivial extensions of tubular algebras
The aim of this note is to give an affirmative answer to a problem raised in [9] by J. Nehring and A. Skowroński, concerning the number of nonstable ℙ₁(K)-families of quasi-tubes in the Auslander-Reiten quivers of the trivial extensions of tubular algebras over algebraically closed fields K.
On the vertices of modules in the Auslander-Reiten quiver.
On the vertices of modules in the Auslander-Reiten quiver II.
On tilting and cotilting-type modules
We use modules of finite length to compare various generalizations of the classical tilting and cotilting modules introduced by Brenner and Butler [BrBu].
On tubes for blocks of wild type
We show that any block of a group algebra of some finite group which is of wild representation type has many families of stable tubes.
On wings of the Auslander-Reiten quivers of selfinjective algebras
We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.
Orbit algebras and periodicity
Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation type.
Orbit algebras that are invariant under stable equivalences of Morita type
In this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.