Tilting theory - an introduction
I. Assem (1990)
Banach Center Publications
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I. Assem (1990)
Banach Center Publications
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Hagen Meltzer (2001)
Colloquium Mathematicae
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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.
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.
Marta Kwiecień, Andrzej Skowroński (2005)
Colloquium Mathematicae
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We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.
Piotr Malicki, José Peña, Andrzej Skowroński (2014)
Open Mathematics
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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.
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.
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...
Alicja Jaworska (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate the categorical behaviour of morphisms between indecomposable projective modules over a special biserial algebra A over an algebraically closed field, which are associated to arrows of the Gabriel quiver of A.
Fidel Hernández Advíncula, Eduardo do Nascimento Marcos (2007)
Colloquium Mathematicae
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The aim of this work is to characterize the algebras which are standardly stratified with respect to any order of the simple modules. We show that such algebras are exactly the algebras with all idempotent ideals projective. We also deduce as a corollary a characterization of hereditary algebras, originally due to Dlab and Ringel.
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.
Mike Prest, Gena Puninski (2004)
Colloquium Mathematicae
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We classify one-directed indecomposable pure injective modules over finite-dimensional string algebras.
Sarah Scherotzke (2009)
Colloquium Mathematicae
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We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. We thereby correct and generalize a result of Farnsteiner [Math. Nachr. 202 (1999)]. Furthermore we show that modules with certain length of composition series are periodic. We apply these results to G-transitive blocks of the universal enveloping algebras of restricted p-Lie algebras and prove that G-transitive principal blocks only...
Marta Kwiecień, Andrzej Skowroński (2009)
Colloquium Mathematicae
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We develop the representation theory of selfinjective algebras of strictly canonical type and prove that their Auslander-Reiten quivers admit quasi-tubes maximally saturated by simple and projective modules.
Dagmar Baer (1986)
Manuscripta mathematica
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Generalov, A.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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Kosovskaya, N.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
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R. Bautista, E. Pérez, L. Salmerón (2011)
Colloquium Mathematicae
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We continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀,...
Jessica Lévesque (2003)
Colloquium Mathematicae
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We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.
Claus Michael Ringel (1990)
Banach Center Publications
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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...
Yoichi Miyashita (1986)
Mathematische Zeitschrift
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Otto Bretscher, C. Läser (1981)
Manuscripta mathematica
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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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