Polynomial growth trivial extensions of simply connected algebras
Jerzy Nehring, Andrzej Skowroński (1989)
Fundamenta Mathematicae
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Jerzy Nehring, Andrzej Skowroński (1989)
Fundamenta Mathematicae
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Ole Enge (2000)
Colloquium Mathematicae
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We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.
Stanisław Kasjan (1998)
Colloquium Mathematicae
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Mirosław Dembiński, Piotr Dowbor, Andrzej Skowroński (1988)
Fundamenta Mathematicae
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Bertha Tomé (1995)
Fundamenta Mathematicae
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Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b)...
Piotr Malicki (1998)
Colloquium Mathematicae
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Zbigniew Leszczyński, Andrzej Skowroński (2000)
Colloquium Mathematicae
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We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.
Daniel Simson (1991)
Fundamenta Mathematicae
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Zygmunt Pogorzały, Karolina Szmyt (2007)
Open Mathematics
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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.
Ibrahim Assem, Yingbo Zhang (1998)
Colloquium Mathematicae
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