The representation dimension of domestic weakly symmetric algebras |
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Authors: | Rafa? Bocian Thorsten Holm Andrzej Skowroński |
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Affiliation: | 1.Faculty of Mathematics and Computer Sciences,Nicolaus Copernicus University,Toruń,Poland;2.Institut für Algebra und Geometrie,Otto-von-Guericke-Universit?t,Magdeburg,Germany |
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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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Keywords: | representation dimension weakly symmetric algebra domestic representation type selfinjective algebra of Euclidean type derived equivalence |
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