The representation dimension of domestic weakly symmetric algebras

• Autorzy: Rafał Bocian , Thorsten Holm , Andrzej Skowroński
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

representation dimension; weakly symmetric algebra; domestic representation type; selfinjective algebra of Euclidean type; derived equivalence; Primary 16D50; 16E10; 16G60; Secondary 16G10; 18E30

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 1
• Strony: 67-75

Daty

wydano

2004-03-01

online

2004-03-01

Twórcy

autor

Rafał Bocian

• Nicolaus Copernicus University

autor

Thorsten Holm

• Otto-von-Guericke-Universität

autor

Andrzej Skowroński

• Nicolaus Copernicus University

Bibliografia

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• [2] R. Bocian, T. Holm and A. Skowroński: “Derived equivalence classification of weakly symmetric algebras of Euclidean type”, Preprint, (2003).
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Identyfikatory

DOI

10.2478/BF02475951