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The representation dimension of domestic weakly symmetric algebras

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Central European Journal of Mathematics

Abstract

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Sciences, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

    Rafał Bocian & Andrzej Skowroński

  2. Institut für Algebra und Geometrie, Otto-von-Guericke-Universität, Postfach 4120, 39016, Magdeburg, Germany

    Thorsten Holm

Authors
  1. Rafał Bocian
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  2. Thorsten Holm
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  3. Andrzej Skowroński
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Bocian, R., Holm, T. & Skowroński, A. The representation dimension of domestic weakly symmetric algebras. centr.eur.j.math. 2, 67–75 (2004). https://doi.org/10.2478/BF02475951

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  • DOI: https://doi.org/10.2478/BF02475951

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