Displaying similar documents to “Selfinjective algebras of wild canonical type”

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.

Selfinjective algebras of tubular type

Jerzy Białkowski, Andrzej Skowroński (2002)

Colloquium Mathematicae

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We classify all tame self/injective algebras having simply connected Galois coverings and the stable Auslander-Reiten quivers consisting of stable tubes. Moreover, the classification of nondomestic polynomial growth standard self/injective algebras is completed.

On nonstandard tame selfinjective algebras having only periodic modules

Jerzy Białkowski, Thorsten Holm, Andrzej Skowroński (2003)

Colloquium Mathematicae

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We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].

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.

On Auslander-Reiten translates in functorially finite subcategories and applications

K. Erdmann, D. Madsen, V. Miemietz (2010)

Colloquium Mathematicae

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We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...

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 T 2 ( A ) of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which T 2 ( A ) is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.

A classification of symmetric algebras of strictly canonical type

Marta Kwiecień, Andrzej Skowroński (2009)

Colloquium Mathematicae

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In continuation of our article in Colloq. Math. 116.1, we give a complete description of the symmetric algebras of strictly canonical type by quivers and relations, using Brauer quivers.

Extremal properties for concealed-canonical algebras

Michael Barot, Dirk Kussin, Helmut Lenzing (2013)

Colloquium Mathematicae

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Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of finite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commutative algebra, algebraic geometry and mathematical physics. We show that canonical algebras are characterized by a number of interesting extremal properties (among concealed-canonical algebras, that is, the endomorphism rings of tilting...

Left-right projective bimodules and stable equivalences of Morita type

Zygmunt Pogorzały (2001)

Colloquium Mathematicae

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We study a connection between left-right projective bimodules and stable equivalences of Morita type for finite-dimensional associative algebras over a field. Some properties of the category of all finite-dimensional left-right projective bimodules for self-injective algebras are also given.

Representation-tame locally hereditary algebras

Zbigniew Leszczyński (2004)

Colloquium Mathematicae

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Let A be a finite-dimensional algebra over an algebraically closed field. The algebra A is called locally hereditary if any local left ideal of A is projective. We give criteria, in terms of the Tits quadratic form, for a locally hereditary algebra to be of tame representation type. Moreover, the description of all representation-tame locally hereditary algebras is completed.

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 restrictions of indecomposables of tame algebras

R. Bautista, E. Pérez, L. Salmerón (2011)

Colloquium Mathematicae

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We continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀,...

Algebras standardly stratified in all orders

Fidel Hernández Advíncula, Eduardo do Nascimento Marcos (2007)

Colloquium Mathematicae

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The aim of this work is to characterize the algebras which are standardly stratified with respect to any order of the simple modules. We show that such algebras are exactly the algebras with all idempotent ideals projective. We also deduce as a corollary a characterization of hereditary algebras, originally due to Dlab and Ringel.

Roots of Nakayama and Auslander-Reiten translations

Helmut Lenzing, Andrzej Skowroński (2000)

Colloquium Mathematicae

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We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.