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1
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On cyclic vertices in valued translation quivers

100%
Malicki P.
Colloquium Mathematicum
|
2006
|
tom 105
|
nr 1
45-50
EN
Let x and y be two vertices lying on an oriented cycle in a connected valued translation quiver (Γ,τ,δ). We prove that, under certain conditions, x and y belong to the same cyclic component of (Γ,τ,δ) if and only if there is an oriented cycle in (Γ,τ,δ) passing through x and y.
2
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Degenerations in the module varieties of almost cyclic coherent Auslander-Reiten components

100%
Malicki P.
Colloquium Mathematicum
|
2009
|
tom 114
|
nr 2
253-276
EN
We establish when the partial orders $≤_{ext}$ and $≤_{deg}$ coincide for all modules of the same dimension from the additive category of a generalized standard almost cyclic coherent component of the Auslander-Reiten quiver of a finite-dimensional algebra.
3
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Generalized coil enlargements of algebras

100%
Malicki P.
Colloquium Mathematicum
|
1998
|
tom 76
|
nr 1
57-83
4
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Hochschild cohomology of generalized multicoil algebras

64%
Malicki P., Skowroński A.
Colloquium Mathematicum
|
2014
|
tom 136
|
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.
5
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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.
6
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On the number of terms in the middle of almost split sequences over cycle-finite artin algebras

51%
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.
7
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Indecomposable modules in coils

51%
Malicki P., Skowroński A., Tomé B.
Colloquium Mathematicum
|
2002
|
tom 93
|
nr 1
67-130
EN
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.
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