Derived tubular algebras and APR-tilts
Hagen Meltzer (2001)
Colloquium Mathematicae
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Hagen Meltzer (2001)
Colloquium Mathematicae
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Mike Prest, Gena Puninski (2004)
Colloquium Mathematicae
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We classify one-directed indecomposable pure injective modules over finite-dimensional string algebras.
Piotr Malicki, Andrzej Skowroński, Bertha Tomé (2002)
Colloquium Mathematicae
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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.
A. Skowronski, I. Assem (1992)
Mathematica Scandinavica
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Otto Kerner, Frank Lukas (1996)
Mathematische Zeitschrift
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Andrzej Skowroński (1984)
Colloquium Mathematicae
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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.
S.P. Smith (1994)
Mathematische Zeitschrift
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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.
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...
Adam Skowyrski (2013)
Colloquium Mathematicae
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We describe the structure of artin algebras for which all cycles of indecomposable modules are finite and almost all indecomposable modules have projective or injective dimension at most one.
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.
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.
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...
J.T. Stafford (1985)
Inventiones mathematicae
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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).
I. Assem (1990)
Banach Center Publications
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John W. Ballard (1978)
Mathematische Zeitschrift
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Manuel Ojanguren, Max-Albert Knus (1975)
Mathematische Zeitschrift
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Andrzej Skowroński, Grzegorz Zwara (1998)
Annales scientifiques de l'École Normale Supérieure
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