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Displaying similar documents to “Generalized coil enlargements of algebras”

Iterated coil enlargements of algebras

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)...

Directing components for quasitilted algebras

Flávio Coelho (1999)

Colloquium Mathematicae

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We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.

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

Grzegorz Bobiński, Andrzej Skowroński (2003)

Open Mathematics

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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...

Tame triangular matrix algebras

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 T 2 ( A ) of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which T 2 ( A ) is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.

A note on tilting sequences

Clezio Braga, Flávio Coelho (2008)

Open Mathematics

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We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.

Quasitilted algebras have preprojective components

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.