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1
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Slice modules over minimal 2-fundamental algebras

100%
Pogorzały Z., Szmyt K.
Open Mathematics
|
2007
|
tom 5
|
nr 1
164-180
EN
We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.
2
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On the number of terms in the middle of almost split sequences over cycle-finite artin algebras

100%
Malicki P., Peña J., Skowroński A.
Open Mathematics
|
2014
|
tom 12
|
nr 1
39-45
EN
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.
3
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On components of the Auslander-Reiten quiver of trivial extensions of 2-fundamental algebras which contain projective modules

100%
Alicja J.
Open Mathematics
|
2007
|
tom 5
|
nr 4
665-685
EN
Trivial extensions of a certain subclass of minimal 2-fundamental algebras are examined. For such algebras the characterization of components of the Auslander-Reiten quiver which contain indecomposable projective modules is given.
4
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Representation theory of two-dimensionalbrauer graph rings

100%
Rump W.
Colloquium Mathematicum
|
2000
|
tom 86
|
nr 2
239-251
EN
We consider a class of two-dimensional non-commutative Cohen-Macaulay rings to which a Brauer graph, that is, a finite graph endowed with a cyclic ordering of edges at any vertex, can be associated in a natural way. Some orders Λ over a two-dimensional regular local ring are of this type. They arise, e.g., as certain blocks of Hecke algebras over the completion of $ℤ[q,q^{-1}]$ at (p,q-1) for some rational prime $p$. For such orders Λ, a class of indecomposable maximal Cohen-Macaulay modules (see introduction) has been determined by K. W. Roggenkamp. We prove that this list of indecomposables of Λ is complete.
5
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Domestic iterated one-point extensions of algebras by two-ray modules

75%
Bobiński G., Skowroński A.
Open Mathematics
|
2003
|
tom 1
|
nr 4
457-476
EN
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 wide class of almost sincere domestic simply connected algebras of large global dimensions.
6
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On a family of vector space categories

63%
Bobiński G., Skowroński A.
Open Mathematics
|
2003
|
tom 1
|
nr 3
332-359
EN
In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.
7
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On artin algebras with almost all indecomposable modules of projective or injective dimension at most one

63%
Skowroński A.
Open Mathematics
|
2003
|
tom 1
|
nr 1
108-122
EN
Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote $$\mathcal{L}_A$$ to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by $$\mathcal{R}_A$$ the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with $$\mathcal{L}_A \cup \mathcal{R}_A$$ co-finite in ind A, quasi-tilted algebras and generalized double tilted algebras, have been extensively investigated. The aim of the paper is to show that these two classes of algebras exhaust the class of all artin algebras A for which $$\mathcal{L}_A \cup \mathcal{R}_A$$ is co-finite in ind A, and derive some consequences.
8
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Classification of discrete derived categories

63%
Bobiński G., Geiß C., Skowroński A.
Open Mathematics
|
2004
|
tom 2
|
nr 1
19-49
EN
The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.
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