Displaying similar documents to “Indecomposable modules in coils”

Tilting slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2008)

Colloquium Mathematicae

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A class of finite-dimensional algebras whose Auslander-Reiten quivers have starting but not generalized standard components is investigated. For these components the slices whose slice modules are tilting are considered. Moreover, the endomorphism algebras of tilting slice modules are characterized.

On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth

Stanisław Kasjan, Grzegorz Pastuszak (2014)

Colloquium Mathematicae

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Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.

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.

On two tame algebras with super-decomposable pure-injective modules

Stanisław Kasjan, Grzegorz Pastuszak (2011)

Colloquium Mathematicae

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Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...

On nonstandard tame selfinjective algebras having only periodic modules

Jerzy Białkowski, Thorsten Holm, Andrzej Skowroński (2003)

Colloquium Mathematicae

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We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].

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...

Relative Auslander-Reiten sequences for quasi-hereditary algebras

Karin Erdmann, José Antonio de la Peña, Corina Sáenz (2002)

Colloquium Mathematicae

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Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).

Limits of tilting modules

Clezio A. Braga, Flávio U. Coelho (2009)

Colloquium Mathematicae

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We study the problem of when a direct limit of tilting modules is still a tilting module.

A note on quasitilted algebras

Andrzej Skowroński, Adam Skowyrski (2014)

Colloquium Mathematicae

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We provide a characterization of artin algebras without chains of nonzero homomorphisms between indecomposable finitely generated modules starting with an injective module and ending with a projective module.

On Auslander-Reiten translates in functorially finite subcategories and applications

K. Erdmann, D. Madsen, V. Miemietz (2010)

Colloquium Mathematicae

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We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...