Minimal Representation-Infinite Coil Algebras.
Ibrahim Assem, Andrzej Skowronski (1990)
Manuscripta mathematica
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Ibrahim Assem, Andrzej Skowronski (1990)
Manuscripta mathematica
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Dieter Happel, Dieter Vossieck (1983)
Manuscripta mathematica
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Flávio U. Coelho, José A. de la Peña, Sonia Trepode (2008)
Colloquium Mathematicae
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A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.
Bernhard Keller (1993)
Manuscripta mathematica
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K. Golema-Hartman (1976)
Colloquium Mathematicae
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Harald Upmeier (1980)
Manuscripta mathematica
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Flávio U. Coelho, Ma. I. R. Martins, Bertha Tomé (2004)
Colloquium Mathematicae
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We study the simple connectedness and strong simple connectedness of the following classes of algebras: (tame) coil enlargements of tame concealed algebras and n-iterated coil enlargement algebras.
Alicja Jaworska-Pastuszak, Andrzej Skowroński (2013)
Colloquium Mathematicae
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We describe the structure of finite-dimensional algebras of domestic representation type over an algebraically closed field whose Auslander-Reiten quiver consists of generalized standard and semiregular components. Moreover, we prove that this class of algebras contains all special biserial algebras whose Auslander-Reiten quiver consists of semiregular components.
Zygmunt Pogorzały, Mirosława Sufranek (2004)
Colloquium Mathematicae
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The class of n-fundamental algebras is introduced. It is a subclass of string algebras. For n-fundamental algebras we study the problem of when the Auslander-Reiten quiver contains, at the beginning or at the end, a component which is not generalized standard.
Christoff Geiss, José A. de de Pena (1995)
Manuscripta mathematica
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S.D. Chatterji (1971)
Manuscripta mathematica
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Harvey Wolff (1975)
Manuscripta mathematica
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Ibrahim Assem (2009)
Colloquium Mathematicae
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We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.
José Isidro, Angel Rodríguez Palacios (1995)
Manuscripta mathematica
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Michael Leinert (1975)
Manuscripta mathematica
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Michael Leinert (1973)
Manuscripta mathematica
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Andrzej Skowroński, Kunio Yamagata (2003)
Colloquium Mathematicae
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We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
Alberto Elduque, José María Pérez (1994)
Manuscripta mathematica
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Andrzej Skowroński, Kunio Yamagata (2015)
Colloquium Mathematicae
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We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
Helmut Röhrl (1977)
Manuscripta mathematica
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