Endomorphism rings of maximal rigid objects in cluster tubes

Dagfinn F. Vatne

Displaying similar documents to “Endomorphism rings of maximal rigid objects in cluster tubes”

Finding a cluster-tilting object for a representation finite cluster-tilted algebra

M. A. Bertani-Økland, S. Oppermann, A. Wrålsen (2010)

Colloquium Mathematicae

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We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.

Morita duality for Grothendieck categories.

José L. Gómez Pardo, Francisco de A. Guil Asensio (1992)

Publicacions Matemàtiques

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We survey some recent results on the theory of Morita duality for Grothendieck categories, comparing two different versions of this concept, and giving applications to QF-3 and Qf-3' rings.

Ladder functors with an application to representation-finite Artinian rings.

Rump, Wolfgang (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Cluster categories for algebras of global dimension 2 and quivers with potential

Claire Amiot (2009)

Annales de l’institut Fourier

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Let $k$ be a field and $A$ a finite-dimensional $k$ -algebra of global dimension $\leq 2$ . We construct a triangulated category $𝒞_{A}$ associated to $A$ which, if $A$ is hereditary, is triangle equivalent to the cluster category of $A$ . When $𝒞_{A}$ is Hom-finite, we prove that it is 2-CY and endowed with a canonical cluster-tilting object. This new class of categories contains some of the stable categories of modules over a preprojective algebra studied by Geiss-Leclerc-Schröer and by Buan-Iyama-Reiten-Scott. Our...

Morita Equivalences of Functor Categories and Decompositions of Functors Defined on a Category Associated to Algebras with One-Side Units

Jolanta Słomińska (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Conditions which imply Morita equivalences of functor categories are described. As an application a Dold-Kan type theorem for functors defined on a category associated to associative algebras with one-side units is proved.

On pure semi-simple Grothendieck categories I

Daniel Simson (1978)

Fundamenta Mathematicae

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Calabi-Yau stable module categories of finite type

Jerzy Białkowski, Andrzej Skowroński (2007)

Colloquium Mathematicae

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We describe the stable module categories of the self-injective finite-dimensional algebras of finite representation type over an algebraically closed field which are Calabi-Yau (in the sense of Kontsevich).

A class of quasitilted rings that are not tilted

Riccardo Colpi, Kent R. Fuller, Enrico Gregorio (2006)

Colloquium Mathematicae

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Based on the work of D. Happel, I. Reiten and S. Smalø on quasitilted artin algebras, the first two authors recently introduced the notion of quasitilted rings. Various authors have presented examples of quasitilted artin algebras that are not tilted. Here we present a class of right quasitilted rings that not right tilted, and we show that they satisfy a condition that would force a quasitilted artin algebra to be tilted.