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].
Andrzej Skowroński, Kunio Yamagata (2015)
Colloquium Mathematicae
Similarity:
We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
Karin Erdmann, Andrzej Skowroński (2015)
Colloquium Mathematicae
Similarity:
We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.
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.
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.
Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
Similarity:
Mazorchuk, Volodymyr (1999)
Beiträge zur Algebra und Geometrie
Similarity:
Andrzej Skowroński (2005)
Colloquium Mathematicae
Similarity:
We construct arbitrarily complicated indecomposable finite-dimensional modules with periodic syzygies over symmetric algebras.
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...
Roberto Cignoli (1972)
Colloquium Mathematicae
Similarity:
B. Węglorz (1970)
Colloquium Mathematicae
Similarity:
Sarah Scherotzke (2009)
Colloquium Mathematicae
Similarity:
We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. We thereby correct and generalize a result of Farnsteiner [Math. Nachr. 202 (1999)]. Furthermore we show that modules with certain length of composition series are periodic. We apply these results to G-transitive blocks of the universal enveloping algebras of restricted p-Lie algebras and prove that G-transitive principal blocks only...
Maciej Karpicz (2011)
Colloquium Mathematicae
Similarity:
We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
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,...
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.
Rafał Bocian, Andrzej Skowroński (2003)
Colloquium Mathematicae
Similarity:
We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.
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.
Marta Kwiecień, Andrzej Skowroński (2009)
Colloquium Mathematicae
Similarity:
We develop the representation theory of selfinjective algebras of strictly canonical type and prove that their Auslander-Reiten quivers admit quasi-tubes maximally saturated by simple and projective modules.
Ibrahim Assem, Andrzej Skowronski (1988)
Mathematische Annalen
Similarity:
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.
Hagen Meltzer (2001)
Colloquium Mathematicae
Similarity:
Zygmunt Pogorzały
Similarity:
CONTENTS1. Introduction.........................................................................................51. The structure of distributive biserial algebras.....................................72. Almost multiplicity-free modules........................................................153. One point extension..........................................................................194. Representation-finite biserial algebras with the (S)-condition...........315. Representation-finite...
Ibrahim Assem, A. Skowronski (1987)
Mathematische Zeitschrift
Similarity:
Rafał Bocian, Thorsten Holm, Andrzej Skowroński (2004)
Open Mathematics
Similarity:
Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional...