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1
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Left-sided quasi-invertible bimodules over Nakayama algebras

100%
Pogorzały Z.
Open Mathematics
|
2005
|
tom 3
|
nr 1
125-142
EN
Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence.
2
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Domestic iterated one-point extensions of algebras by two-ray modules

86%
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.
3
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Squared cycles in monomial relations algebras

86%
Jue B.
Open Mathematics
|
2006
|
tom 4
|
nr 2
250-259
EN
Let $$\mathbb{K}$$ be an algebraically closed field. Consider a finite dimensional monomial relations algebra $$\Lambda = {{\mathbb{K}\Gamma } \mathord{\left/ {\vphantom {{\mathbb{K}\Gamma } I}} \right. \kern-\nulldelimiterspace} I}$$ of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path algebra $$\mathbb{K}\Gamma $$ . There are many modules over Λ which may be represented graphically by a tree with respect to a top element, of which the indecomposable projectives are the most natural example. These trees possess branches which correspond to right subpaths of cycles in the quiver. A pattern in the syzygies of a specific factor module of the corresponding indecomposable projective module is found, allowing us to conclude that the square of any cycle must lie in the ideal I.
4
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On a family of vector space categories

72%
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.
5
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Classification of discrete derived categories

72%
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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