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Zbigniew Leszczyński (2002)
Colloquium Mathematicae
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We prove that a completely separating incidence algebra of a partially ordered set is of tame representation type if and only if the associated Tits integral quadratic form is weakly non-negative.
L. Fuchs (1966)
Colloquium Mathematicae
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B. Węglorz (1970)
Colloquium Mathematicae
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Roberto Cignoli (1972)
Colloquium Mathematicae
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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.
Stanisław Kasjan (2002)
Fundamenta Mathematicae
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Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.
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.
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.
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.
Rafał Bocian, Thorsten Holm, Andrzej Skowroński (2004)
Open Mathematics
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Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional...
Stanislaw Kasjan (2002)
Colloquium Mathematicae
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We apply van den Dries's test to the class of algebras (over algebraically closed fields) which are not representation-directed and prove that this class is axiomatizable by a positive quantifier-free formula. It follows that the representation-directed algebras form an open ℤ-scheme.
Zbigniew Leszczyński (2004)
Colloquium Mathematicae
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Let A be a finite-dimensional algebra over an algebraically closed field. The algebra A is called locally hereditary if any local left ideal of A is projective. We give criteria, in terms of the Tits quadratic form, for a locally hereditary algebra to be of tame representation type. Moreover, the description of all representation-tame locally hereditary algebras is completed.
P. Kratochvil (1971)
Colloquium Mathematicae
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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.
Mazorchuk, Volodymyr (1999)
Beiträge zur Algebra und Geometrie
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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.
Camillo Trapani (2005)
Banach Center Publications
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The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized. ...
Ibrahim Assem, A. Skowronski (1987)
Mathematische Zeitschrift
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Panaiotis K. Pavlakos (1990)
Mathematische Annalen
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Milan Sekanina (1970)
Colloquium Mathematicae
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Marta Błaszkiewicz, Andrzej Skowroński (2012)
Colloquium Mathematicae
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We describe the structure of finite-dimensional self-injective algebras of finite representation type over a field whose stable Auslander-Reiten quiver has a sectional module not lying on a short chain.
Andrzej Skowronski, Josef Waschbüsch (1983)
Journal für die reine und angewandte Mathematik
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Noriaki Kamiya, Daniel Mondoc, Susumu Okubo (2011)
Banach Center Publications
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In this paper we give a review on δ-structurable algebras. A connection between Malcev algebras and a generalization of δ-structurable algebras is also given.
Tvalavadze, Marina (2012)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: Primary 17D15. Secondary 17D05, 17B35, 17A99. This is a survey paper to summarize the latest results on the universal enveloping algebras of Malcev algebras, triple systems and Leibniz n-ary algebras.
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.