Selfinjective and Simply Connected Algebras.
Otto Bretscher, C. Läser (1981)
Manuscripta mathematica
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Otto Bretscher, C. Läser (1981)
Manuscripta mathematica
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Nikolaos Marmaridis (1984)
Manuscripta mathematica
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Hagen Meltzer (2001)
Colloquium Mathematicae
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Jie Du (1992)
Manuscripta mathematica
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Piotr Malicki, Andrzej Skowroński, Bertha Tomé (2002)
Colloquium Mathematicae
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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.
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.
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...
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.
A. Skowronski, I. Assem (1992)
Mathematica Scandinavica
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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.
Jessica Lévesque (2003)
Colloquium Mathematicae
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We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.
Mike Prest, Gena Puninski (2004)
Colloquium Mathematicae
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We classify one-directed indecomposable pure injective modules over finite-dimensional string algebras.
Piotr Malicki, José Peña, Andrzej Skowroński (2014)
Open Mathematics
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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.
Andrzej Skowroński (1984)
Colloquium Mathematicae
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Adam Skowyrski (2013)
Colloquium Mathematicae
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We describe the structure of artin algebras for which all cycles of indecomposable modules are finite and almost all indecomposable modules have projective or injective dimension at most one.
Grzegorz Bobiński, Andrzej Skowroński (2003)
Open Mathematics
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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...
William Crawley-Boevey, Otto Kerner (1994)
Mathematische Annalen
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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.
I. Assem (1990)
Banach Center Publications
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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.
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.
Otto Kerner, Frank Lukas (1996)
Mathematische Zeitschrift
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