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Representation Dimension of Cluster-Concealed Algebras

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Abstract

We prove that the representation dimension of a cluster-concealed algebra B is three. We compute its representation dimension by showing an explicit Auslander generator for the cluster-tilted algebra.

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Authors and Affiliations

  1. Depto de Matemática, FCEyN, Universidad Nacional de Mar del Plata, 7600, Mar del Plata, Argentina

    Alfredo González Chaio

  2. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Funes 3350, Universidad Nacional de Mar del Plata, 7600, Mar del Plata, Argentina

    Sonia Trepode

Authors
  1. Alfredo González Chaio
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  2. Sonia Trepode
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Correspondence to Sonia Trepode.

Additional information

This work is part of the Phd Thesis of Alfredo Gonzalez Chaio, under the supervision of Sonia Trepode, in course at Universidad Nacional de Mar del Plata. The first author was supported by a grant from CONICET. The second author is a researcher of CONICET, Argentina. We would like to thank the referee for the very useful suggestions that let us simplify some proofs and improve the form of this article.

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González Chaio, A., Trepode, S. Representation Dimension of Cluster-Concealed Algebras. Algebr Represent Theor 16, 1001–1015 (2013). https://doi.org/10.1007/s10468-012-9343-5

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  • DOI: https://doi.org/10.1007/s10468-012-9343-5

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