On the problem of axiomatization of tame representation type

Stanisław Kasjan

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Displaying similar documents to “On the problem of axiomatization of tame representation type”

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Alicja Jaworska-Pastuszak, Andrzej Skowroński (2013)

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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.

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Zygmunt Pogorzały, Mirosława Sufranek (2004)

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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.

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Andrzej Skowroński, Kunio Yamagata (2003)

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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.

Orthogonal Gelfand-Zetlin algebras. I.

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Left sections and the left part of an artin algebra

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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.

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Some remarks on Post algebras

R. Beazer (1974)

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A note on Post algebras

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On selfinjective algebras of tilted type

Andrzej Skowroński, Kunio Yamagata (2015)

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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.

The class of 2-dimensional neat reducts is not elementary

Tarek Sayed Ahmed (2002)

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SC, CA, QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras and Halmos' quasipolyadic algebras with equality, respectively. Generalizing a result of Andréka and Németi on cylindric algebras, we show that for K ∈ SC,QA,CA,QEA and any β > 2 the class of 2-dimensional neat reducts of β-dimensional algebras in K is not closed under forming elementary subalgebras, hence is not elementary. Whether this result extends...

CB-degenerations and rigid degenerations of algebras

Adam Hajduk (2006)

Colloquium Mathematicae

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The main aim of this note is to prove that if k is an algebraically closed field and a k-algebra A₀ is a CB-degeneration of a finite-dimensional k-algebra A₁, then there exists a factor algebra Ā₀ of A₀ of the same dimension as A₁ such that Ā₀ is a CB-degeneration of A₁. As a consequence, Ā₀ is a rigid degeneration of A₁, provided A₀ is basic.