Wild Hereditary Artin Algebras and Linear Methods.
Dagmar Baer (1986)
Manuscripta mathematica
Similarity:
Dagmar Baer (1986)
Manuscripta mathematica
Similarity:
K. Erdmann, D. Madsen, V. Miemietz (2010)
Colloquium Mathematicae
Similarity:
We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...
Hagen Meltzer (2001)
Colloquium Mathematicae
Similarity:
Piotr Malicki, Andrzej Skowroński, Bertha Tomé (2002)
Colloquium Mathematicae
Similarity:
We describe the structure of all indecomposable modules in standard coils of the Auslander-Reiten quivers of finite-dimensional algebras over an algebraically closed field. We prove that the supports of such modules are obtained from algebras with sincere standard stable tubes by adding braids of two linear quivers. As an application we obtain a complete classification of non-directing indecomposable modules over all strongly simply connected algebras of polynomial growth.
Zygmunt Pogorzały, Karolina Szmyt (2008)
Colloquium Mathematicae
Similarity:
A class of finite-dimensional algebras whose Auslander-Reiten quivers have starting but not generalized standard components is investigated. For these components the slices whose slice modules are tilting are considered. Moreover, the endomorphism algebras of tilting slice modules are characterized.
A. Skowronski, I. Assem (1992)
Mathematica Scandinavica
Similarity:
Flávio Coelho (1999)
Colloquium Mathematicae
Similarity:
We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.
Jie Du (1992)
Manuscripta mathematica
Similarity:
Grzegorz Bobiński, Andrzej Skowroński (2003)
Open Mathematics
Similarity:
In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a...
Zbigniew Leszczyński, Andrzej Skowroński (2000)
Colloquium Mathematicae
Similarity:
We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.
Dieter Happel, Dieter Vossieck (1983)
Manuscripta mathematica
Similarity:
Ibrahim Assem (2009)
Colloquium Mathematicae
Similarity:
We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.
Nikolaos Marmaridis (1984)
Manuscripta mathematica
Similarity:
Andrzej Skowroński, Kunio Yamagata (2003)
Colloquium Mathematicae
Similarity:
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.
Marta Kwiecień, Andrzej Skowroński (2005)
Colloquium Mathematicae
Similarity:
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.
Otto Kerner (1988)
Manuscripta mathematica
Similarity:
Jerzy Białkowski, Thorsten Holm, Andrzej Skowroński (2003)
Colloquium Mathematicae
Similarity:
We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].
Stanisław Kasjan, Grzegorz Pastuszak (2014)
Colloquium Mathematicae
Similarity:
Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.
Piotr Malicki, José Peña, Andrzej Skowroński (2014)
Open Mathematics
Similarity:
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.
Alicja Jaworska-Pastuszak, Andrzej Skowroński (2013)
Colloquium Mathematicae
Similarity:
We describe the structure of finite-dimensional algebras of domestic representation type over an algebraically closed field whose Auslander-Reiten quiver consists of generalized standard and semiregular components. Moreover, we prove that this class of algebras contains all special biserial algebras whose Auslander-Reiten quiver consists of semiregular components.
Zygmunt Pogorzały, Mirosława Sufranek (2004)
Colloquium Mathematicae
Similarity:
The class of n-fundamental algebras is introduced. It is a subclass of string algebras. For n-fundamental algebras we study the problem of when the Auslander-Reiten quiver contains, at the beginning or at the end, a component which is not generalized standard.
Grzegorz Bobiński, Andrzej Skowroński (2001)
Colloquium Mathematicae
Similarity:
We give a complete description of finite-dimensional selfinjective algebras of Euclidean tilted type over an algebraically closed field whose all nonperiodic Auslander-Reiten components are almost regular. In particular, we describe the tame selfinjective finite-dimensional algebras whose all nonperiodic Auslander-Reiten components are almost regular and generalized standard.
Jerzy Białkowski, Andrzej Skowroński, Adam Skowyrski, Paweł Wiśniewski (2012)
Colloquium Mathematicae
Similarity:
We describe the structure of artin algebras for which all cycles of indecomposable finitely generated modules are finite and all Auslander-Reiten components are semiregular.