On tame repetitive algebras
Ibrahim Assem, Andrzej Skowroński (1993)
Fundamenta Mathematicae
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Displaying similar documents to “Algebra invariants for finite directed graphs with relations.”
On tame repetitive algebras
On quasitilted algebras which are one-point extensions of hereditary algebras
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.
On matrices over -algebras.
Moslehian, M.S. (2003)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Incidence algebras and algebraic fundamental group.
Reynaud, Eric (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Starting and ending components of the Auslander-Reiten quivers of a class of special biserial 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.
Finiteness of the strong global dimension of radical square zero algebras
Otto Kerner, Andrzej Skowroński, Kunio Yamagata, Dan Zacharia (2004)
Open Mathematics
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The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem...
On graph -algebras with a linear ideal lattice.
Eilers, Søren, Restor, Gunnar, Ruiz, Efren (2010)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Finitary axiomatizations of the true relational equations
Roger Maddux (1993)
Banach Center Publications
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Comtrans algebras and their physical applications
Jonathan Smith (1993)
Banach Center Publications
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On domestic algebras of semiregular type
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.
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...
Full matrix algebras with structure systems
Hisaaki Fujita (2003)
Colloquium Mathematicae
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We study associative, basic n × n𝔸-full matrix algebras over a field, whose multiplications are determined by structure systems 𝔸, that is, n-tuples of n × n matrices with certain properties.
Tame triangular matrix algebras
Zbigniew Leszczyński, Andrzej Skowroński (2000)
Colloquium Mathematicae
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We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.
Left sections and the left part of an artin algebra
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.
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...
Cycle-finite algebras of semiregular type
Jerzy Białkowski, Andrzej Skowroński, Adam Skowyrski, Paweł Wiśniewski (2012)
Colloquium Mathematicae
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We describe the structure of artin algebras for which all cycles of indecomposable finitely generated modules are finite and all Auslander-Reiten components are semiregular.