Displaying similar documents to “On nonstandard tame selfinjective algebras having only periodic modules”

Indecomposable modules in coils

Piotr Malicki, Andrzej Skowroński, Bertha Tomé (2002)

Colloquium Mathematicae

Similarity:

We describe the structure of all indecomposable modules in standard coils of the Auslander-Reiten quivers of finite-dimensional algebras over an algebraically closed field. We prove that the supports of such modules are obtained from algebras with sincere standard stable tubes by adding braids of two linear quivers. As an application we obtain a complete classification of non-directing indecomposable modules over all strongly simply connected algebras of polynomial growth.

On two tame algebras with super-decomposable pure-injective modules

Stanisław Kasjan, Grzegorz Pastuszak (2011)

Colloquium Mathematicae

Similarity:

Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...

The periodicity conjecture for blocks of group algebras

Karin Erdmann, Andrzej Skowroński (2015)

Colloquium Mathematicae

Similarity:

We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.

Selfinjective algebras of strictly canonical type

Marta Kwiecień, Andrzej Skowroński (2009)

Colloquium Mathematicae

Similarity:

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.

Tilting slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2008)

Colloquium Mathematicae

Similarity:

A class of finite-dimensional algebras whose Auslander-Reiten quivers have starting but not generalized standard components is investigated. For these components the slices whose slice modules are tilting are considered. Moreover, the endomorphism algebras of tilting slice modules are characterized.

Selfinjective algebras of tubular type

Jerzy Białkowski, Andrzej Skowroński (2002)

Colloquium Mathematicae

Similarity:

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.

Left sections and the left part of an artin algebra

Ibrahim Assem (2009)

Colloquium Mathematicae

Similarity:

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.

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

Grzegorz Bobiński, Andrzej Skowroński (2001)

Colloquium Mathematicae

Similarity:

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.

Directing components for quasitilted algebras

Flávio Coelho (1999)

Colloquium Mathematicae

Similarity:

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.

Orbit algebras and periodicity

Petter Andreas Bergh (2009)

Colloquium Mathematicae

Similarity:

Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation type.

Euclidean components for a class of self-injective algebras

Sarah Scherotzke (2009)

Colloquium Mathematicae

Similarity:

We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. We thereby correct and generalize a result of Farnsteiner [Math. Nachr. 202 (1999)]. Furthermore we show that modules with certain length of composition series are periodic. We apply these results to G-transitive blocks of the universal enveloping algebras of restricted p-Lie algebras and prove that G-transitive principal blocks only...

On domestic algebras of semiregular type

Alicja Jaworska-Pastuszak, Andrzej Skowroński (2013)

Colloquium Mathematicae

Similarity:

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.

Cycle-finite algebras of semiregular type

Jerzy Białkowski, Andrzej Skowroński, Adam Skowyrski, Paweł Wiśniewski (2012)

Colloquium Mathematicae

Similarity:

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.

Iterated tilted and tilted stably hereditary algebras

Jessica Lévesque (2003)

Colloquium Mathematicae

Similarity:

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.

On Auslander-Reiten translates in functorially finite subcategories and applications

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

Colloquium Mathematicae

Similarity:

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...

On wings of the Auslander-Reiten quivers of selfinjective algebras

Marta Kwiecień, Andrzej Skowroński (2005)

Colloquium Mathematicae

Similarity:

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.

Symmetric special biserial algebras of euclidean type

Rafał Bocian, Andrzej Skowroński (2003)

Colloquium Mathematicae

Similarity:

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

Tame triangular matrix algebras

Zbigniew Leszczyński, Andrzej Skowroński (2000)

Colloquium Mathematicae

Similarity:

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.

On split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia (2003)

Colloquium Mathematicae

Similarity:

Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.

On selfinjective algebras of tilted type

Andrzej Skowroński, Kunio Yamagata (2015)

Colloquium Mathematicae

Similarity:

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.

Strongly simply connected coil algebras

Flávio U. Coelho, Ma. I. R. Martins, Bertha Tomé (2004)

Colloquium Mathematicae

Similarity:

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.