Representation-finite triangular algebras form an open scheme

Stanisław Kasjan

Displaying similar documents to “Representation-finite triangular algebras form an open scheme”

On a family of vector space categories

Grzegorz Bobiński, Andrzej Skowroński (2003)

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In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten...

Degenerations for modules over representation-finite selfinjective algebras

Grzegorz Zwara (1998)

Colloquium Mathematicae

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Substructures of algebras with weakly non-negative Tits form.

José Antonio de la Peña, Andrzej Skowronski (2007)

Extracta Mathematicae

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Let A = kQ/I be a finite dimensional basic algebra over an algebraically closed field k presented by its quiver Q with relations I. A fundamental problem in the representation theory of algebras is to decide whether or not A is of tame or wild type. In this paper we consider triangular algebras A whose quiver Q has no oriented paths. We say that A is essentially sincere if there is an indecomposable (finite dimensional) A-module whose support contains all extreme vertices of Q. We prove...

On the numbers of discrete indecomposable modules over tame algebras

Andrzej Skowroński, Grzegorz Zwara (1997)

Colloquium Mathematicae

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Classification of discrete derived categories

Grzegorz Bobiński, Christof Geiß, Andrzej Skowroński (2004)

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The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.

Tame minimal non-polynomial growth simply connected algebras

Rainer Nörenberg, Andrzej Skowroński (1997)

Colloquium Mathematicae

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Partial flag varieties and preprojective algebras

Christof Geiß, Bernard Leclerc, Jan Schröer (2008)

Annales de l’institut Fourier

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Let $Λ$ be a preprojective algebra of type $A, D, E$ , and let $G$ be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories $Sub Q$ for $Q$ an injective $Λ$ -module, and we introduce a mutation operation between complete rigid modules in $Sub Q$ . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to $G$ .

Constructing the directing components of an algebra

J. de la Peña, M. Takane (1997)

Colloquium Mathematicae

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On some formulas in the Hall algebra of the Kronecker algebra.

Szántó, Csaba (2007)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Cartan matrices of selfinjective algebras of tubular type

Jerzy Białkowski (2004)

Open Mathematics

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The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective algebras having simply connected Galois coverings and the stable Auslander-Reiten...