Marta Kwiecień, Andrzej Skowroński (2005)
Colloquium Mathematicae
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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.
Zygmunt Pogorzały, Mirosława Sufranek (2004)
Colloquium Mathematicae
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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
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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
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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
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Alicja Jaworska-Pastuszak, Andrzej Skowroński (2013)
Colloquium Mathematicae
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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.
Andrzej Skowroński, Kunio Yamagata (2015)
Colloquium Mathematicae
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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.
Hagen Meltzer (2001)
Colloquium Mathematicae
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Jerzy Białkowski, Andrzej Skowroński, Adam Skowyrski, Paweł Wiśniewski (2012)
Colloquium Mathematicae
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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.
Grzegorz Bobiński, Andrzej Skowroński (2001)
Colloquium Mathematicae
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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.
K. Erdmann, D. Madsen, V. Miemietz (2010)
Colloquium Mathematicae
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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...
Fidel Hernández Advíncula, Eduardo do Nascimento Marcos (2007)
Colloquium Mathematicae
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The aim of this work is to characterize the algebras which are standardly stratified with respect to any order of the simple modules. We show that such algebras are exactly the algebras with all idempotent ideals projective. We also deduce as a corollary a characterization of hereditary algebras, originally due to Dlab and Ringel.
Rafał Bocian, Andrzej Skowroński (2003)
Colloquium Mathematicae
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We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.
Marta Kwiecień, Andrzej Skowroński (2009)
Colloquium Mathematicae
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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.
I. Assem (1990)
Banach Center Publications
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Dagmar Baer (1986)
Manuscripta mathematica
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Flávio Coelho (1999)
Colloquium Mathematicae
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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.
Marta Błaszkiewicz, Andrzej Skowroński (2012)
Colloquium Mathematicae
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We describe the structure of finite-dimensional self-injective algebras of finite representation type over a field whose stable Auslander-Reiten quiver has a sectional module not lying on a short chain.
Zygmunt Pogorzały
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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...
Zygmunt Pogorzały, Karolina Szmyt (2008)
Colloquium Mathematicae
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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.
Ibrahim Assem, A. Skowronski (1987)
Mathematische Zeitschrift
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Flávio U. Coelho, Ma. I. R. Martins, Bertha Tomé (2004)
Colloquium Mathematicae
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We study the simple connectedness and strong simple connectedness of the following classes of algebras: (tame) coil enlargements of tame concealed algebras and n-iterated coil enlargement algebras.
Flávio U. Coelho, José A. de la Peña, Sonia Trepode (2008)
Colloquium Mathematicae
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A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.
Noriaki Kamiya, Daniel Mondoc, Susumu Okubo (2011)
Banach Center Publications
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In this paper we give a review on δ-structurable algebras. A connection between Malcev algebras and a generalization of δ-structurable algebras is also given.
Justyna Kosakowska (2009)
Colloquium Mathematicae
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We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.
Rost, Markus (1996)
Documenta Mathematica
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M. G. Stone (1975)
Colloquium Mathematicae
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R. Bautista, E. Pérez, L. Salmerón (2011)
Colloquium Mathematicae
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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,...
Daniel W. Stroock (1976)
Colloquium Mathematicae
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