Displaying similar documents to “Cycle-finite algebras of semiregular type”

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.

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.

On selfinjective algebras of tilted type

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.

Selfinjective algebras of euclidean type with almost regular nonperiodic Auslander-Reiten components

Grzegorz Bobiński, Andrzej Skowroński (2001)

Colloquium Mathematicae

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We give a complete description of finite-dimensional selfinjective algebras of Euclidean tilted type over an algebraically closed field whose all nonperiodic Auslander-Reiten components are almost regular. In particular, we describe the tame selfinjective finite-dimensional algebras whose all nonperiodic Auslander-Reiten components are almost regular and generalized standard.

Strongly simply connected coil algebras

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.

On derived equivalence classification of gentle two-cycle algebras

Grzegorz Bobiński, Piotr Malicki (2008)

Colloquium Mathematicae

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We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.

On wings of the Auslander-Reiten quivers of selfinjective algebras

Marta Kwiecień, Andrzej Skowroński (2005)

Colloquium Mathematicae

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We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.

Iterated tilted and tilted stably hereditary algebras

Jessica Lévesque (2003)

Colloquium Mathematicae

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We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.

A review on δ-structurable algebras

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.

On minimal non-tilted 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.

Selfinjective algebras of strictly canonical type

Marta Kwiecień, Andrzej Skowroński (2009)

Colloquium Mathematicae

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We develop the representation theory of selfinjective algebras of strictly canonical type and prove that their Auslander-Reiten quivers admit quasi-tubes maximally saturated by simple and projective modules.

On self-injective algebras of finite representation type

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.

Directing components for quasitilted algebras

Flávio Coelho (1999)

Colloquium Mathematicae

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We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.

Symmetric special biserial algebras of euclidean type

Rafał Bocian, Andrzej Skowroński (2003)

Colloquium Mathematicae

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We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.