On tame repetitive algebras
Ibrahim Assem, Andrzej Skowroński (1993)
Fundamenta Mathematicae
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Ibrahim Assem, Andrzej Skowroński (1993)
Fundamenta Mathematicae
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Helmut Lenzing, Andrzej Skowroński (1999)
Colloquium Mathematicae
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Dieter Happel, Inger Slungård (1999)
Colloquium Mathematicae
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Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.
Grzegorz Bobiński, Andrzej Skowroński (2003)
Open Mathematics
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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...
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...
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...
Hagen Meltzer (1996)
Colloquium Mathematicae
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Grzegorz Zwara (1998)
Colloquium Mathematicae
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Sergio Albeverio, Bakhrom A. Omirov, Isamiddin S. Rakhimov (2006)
Extracta Mathematicae
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L. Torkzadeh, M. M. Zahedi (2006)
Mathware and Soft Computing
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In this note we classify the bounded hyper K-algebras of order 3, which have D = {1}, D = {1,2} and D = {0,1} as a dual commutative hyper K-ideal of type 1. In this regard we show that there are such non-isomorphic bounded hyper K-algebras.