Minimal Representation-Infinite Coil Algebras.
Ibrahim Assem, Andrzej Skowronski (1990)
Manuscripta mathematica
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Ibrahim Assem, Andrzej Skowronski (1990)
Manuscripta mathematica
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Otto Kerner (1988)
Manuscripta mathematica
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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.
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 (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.
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.
K. Golema-Hartman (1976)
Colloquium Mathematicae
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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.
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.
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.
Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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B. Węglorz (1970)
Colloquium Mathematicae
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Roberto Cignoli (1972)
Colloquium Mathematicae
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Otto Bretscher, C. Läser (1981)
Manuscripta mathematica
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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.
Bernhard Keller (1993)
Manuscripta mathematica
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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.
Ibrahim Assem, A. Skowronski (1987)
Mathematische Zeitschrift
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Mazorchuk, Volodymyr (1999)
Beiträge zur Algebra und Geometrie
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Harald Upmeier (1980)
Manuscripta mathematica
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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.
Dagmar Baer (1986)
Manuscripta mathematica
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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.