Tame algebras with strongly simply connected Galois coverings
Andrzej Skowroński (1997)
Colloquium Mathematicae
Similarity:
Andrzej Skowroński (1997)
Colloquium Mathematicae
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.
Jerzy Nehring, Andrzej Skowroński (1989)
Fundamenta Mathematicae
Similarity:
Piotr Malicki (1998)
Colloquium Mathematicae
Similarity:
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.
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.
M. Barot, J. de la Peña (1999)
Colloquium Mathematicae
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...
Bertha Tomé (1995)
Fundamenta Mathematicae
Similarity:
Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b)...
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.
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.
Otto Bretscher, C. Läser (1981)
Manuscripta mathematica
Similarity:
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.
R. Bautista, E. Pérez, L. Salmerón (2011)
Colloquium Mathematicae
Similarity:
We continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀,...