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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Projective abelian Hopf algebras over a field

100%
Skowroński A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction............................................................................................................................................5 1. Cohen schemes.................................................................................................................................7 2. Projective abelian Hopf algebras......................................................................................................11 3. The structure of groups $Hom_{ℋ ₁}(^mP,^nP)$..............................................................................17 4. Endomorphism rings of $^nP$..........................................................................................................27 5. The $End_{ℋ ₁}(^nP) - End_{ℋ ₁}(^mP)$-bimodule structure of $Hom_{ℋ ₁}(^mP,^nP)$................31 References..........................................................................................................................................42
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Generalized canonical algebras and standard stable tubes

93%
Skowroński A.
Colloquium Mathematicum
|
2001
|
tom 90
|
nr 1
77-93
EN
We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.
3
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Tame algebras with strongly simply connected Galois coverings

93%
Skowroński A.
Colloquium Mathematicum
|
1997
|
tom 72
|
nr 2
335-351
4
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On artin algebras with almost all indecomposable modules of projective or injective dimension at most one

93%
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.
5
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A construction of complex syzygy periodic modules over symmetric algebras

93%
Skowroński A.
Colloquium Mathematicum
|
2005
|
tom 103
|
nr 1
61-69
EN
We construct arbitrarily complicated indecomposable finite-dimensional modules with periodic syzygies over symmetric algebras.
6
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The global basie dimension of artin rings

66%
Meltzer H., Skowroński A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction.............5 2. Basic dimension of artin rings................7 3. Cobasic dimension of artin rings............8 4. Basic dimension of algebras stably equivalent to an hereditary artin algebra............12 5. Hereditary artin algebras of global basic and cobasic dimension 1....................17 6. Global basic and cobasic dimensions of radical squared zero algebras............34 References...............43
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On tame repetitive algebras

60%
Assem I., Skowroński A.
Fundamenta Mathematicae
|
1993
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tom 142
|
nr 1
59-84
EN
Let A be a finite dimensional algebra over an algebraically closed field, and denote by T(A) (respectively, Â) the trivial extension of A by its minimal injective cogenerator bimodule (respectively, the repetitive algebra of A). We characterise the algebras A such that  is tame and exhaustive, that is, the push-down functor mod  → mod T(A) associated with the covering functor  → T(A)\nsimto Â/(ν_A)$ is dense. We show that, if  is tame and exhaustive, then A is simply connected if and only if A is not an iterated tilted algebra of type $Â_m$. Then we prove that  is tame and exhaustive if and only if A is tilting-cotilting equivalent to an algebra which is either hereditary of Dynkin or Euclidean type or is tubular canonical.
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Selfinjective algebras of euclidean type with almost regular nonperiodic Auslander-Reiten components

60%
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.
9
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A general form of non-Frobenius self-injective algebras

60%
Skowroński A., Yamagata K.
Colloquium Mathematicum
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2006
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tom 105
|
nr 1
135-141
EN
Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.
10
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Calabi-Yau stable module categories of finite type

60%
Białkowski J., Skowroński A.
Colloquium Mathematicum
|
2007
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tom 109
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nr 2
257-269
EN
We describe the stable module categories of the self-injective finite-dimensional algebras of finite representation type over an algebraically closed field which are Calabi-Yau (in the sense of Kontsevich).
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On Auslander–Reiten components for quasitilted algebras

60%
Coelho F. U., Skowroński A.
Fundamenta Mathematicae
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1996
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tom 149
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nr 1
67-82
EN
An artin algebra A over a commutative artin ring R is called quasitilted if gl.dim A ≤ 2 and for each indecomposable finitely generated A-module M we have pd M ≤ 1 or id M ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander-Reiten quiver $Γ_A$ of a quasitilted algebra A.
12
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On domestic algebras of semiregular type

60%
Jaworska-Pastuszak A., Skowroński A.
Colloquium Mathematicum
|
2013
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tom 132
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nr 2
271-294
EN
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.
13
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Hochschild cohomology of generalized multicoil algebras

60%
Malicki P., Skowroński A.
Colloquium Mathematicum
|
2014
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tom 136
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nr 2
231-254
EN
We determine the Hochschild cohomology of all finite-dimensional generalized multicoil algebras over an algebraically closed field, which are the algebras for which the Auslander-Reiten quiver admits a separating family of almost cyclic coherent components. In particular, the analytically rigid generalized multicoil algebras are described.
14
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Symmetric special biserial algebras of euclidean type

60%
Bocian R., Skowroński A.
Colloquium Mathematicum
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2003
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tom 96
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nr 1
121-148
EN
We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.
15
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The periodicity conjecture for blocks of group algebras

60%
Erdmann K., Skowroński A.
Colloquium Mathematicum
|
2015
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tom 138
|
nr 2
283-294
EN
We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.
16
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Derived equivalence classification of weakly symmetric algebras of domestic type

60%
Bocian R., Skowroński A.
Colloquium Mathematicum
|
2016
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tom 142
|
nr 1
115-133
EN
We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.
17
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Geometry of modules over tame quasi-tilted algebras

60%
Bobiński G., Skowroński A.
Colloquium Mathematicum
|
1999
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tom 79
|
nr 1
85-118
18
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On selfinjective algebras of tilted type

60%
Skowroński A., Yamagata K.
Colloquium Mathematicum
|
2015
|
tom 141
|
nr 1
89-117
EN
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.
19
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Selfinjective algebras of strictly canonical type

60%
Kwiecień M., Skowroński A.
Colloquium Mathematicum
|
2009
|
tom 116
|
nr 1
47-103
EN
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.
20
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A classification of symmetric algebras of strictly canonical type

60%
Kwiecień M., Skowroński A.
Colloquium Mathematicum
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2009
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tom 116
|
nr 2
249-271
EN
In continuation of our article in Colloq. Math. 116.1, we give a complete description of the symmetric algebras of strictly canonical type by quivers and relations, using Brauer quivers.
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