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1
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On additive functions for stable translation quivers

100%
Bobiński G.
Colloquium Mathematicum
|
1999
|
tom 79
|
nr 2
203-210
EN
The aim of this note is to give a complete description of the positive additive functions for the stable nonperiodic translation quivers with finitely many orbits. In particular, we show that all positive additive functions on the stable translation quivers of Euclidean type (respectively, of wild type) are periodic, and hence bounded (respectively, are unbounded, and hence nonperiodic).
2
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Selfinjective algebras of euclidean type with almost regular nonperiodic Auslander-Reiten components

64%
Bobiński G., Skowroński A.
Colloquium Mathematicum
|
2001
|
tom 88
|
nr 1
93-120
EN
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.
3
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Schubert varieties and representations of Dynkin quivers

64%
Bobiński G., Zwara G.
Colloquium Mathematicum
|
2002
|
tom 94
|
nr 2
285-309
EN
We show that the types of singularities of Schubert varieties in the flag varieties Flagₙ, n ∈ ℕ, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔸. Similarly, we prove that the types of singularities of Schubert varieties in products of Grassmannians Grass(n,a) × Grass(n,b), a, b, n ∈ ℕ, a, b ≤ n, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔻. We also show that the orbit closures in representation varieties of Dynkin quivers of type 𝔻 are normal and Cohen-Macaulay varieties.
4
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On derived equivalence classification of gentle two-cycle algebras

64%
Bobiński G., Malicki P.
Colloquium Mathematicum
|
2008
|
tom 112
|
nr 1
33-72
EN
We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.
5
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Geometry of modules over tame quasi-tilted algebras

64%
Bobiński G., Skowroński A.
Colloquium Mathematicum
|
1999
|
tom 79
|
nr 1
85-118
6
Content available remote

On a family of vector space categories

64%
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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Domestic iterated one-point extensions of algebras by two-ray modules

64%
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.
8
Content available remote

Classification of discrete derived categories

51%
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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