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On nonstandard tame selfinjective algebras having only periodic modules

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Białkowski J., Holm T., Skowroński A.

Colloquium Mathematicum

2003

tom 97

nr 1

33-47

We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].

The representation dimension of domestic weakly symmetric algebras

100%

Bocian R., Holm T., Skowroński A.

Open Mathematics

2004

tom 2

nr 1

67-75

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

2 Holm T.

2 Skowroński A.

1 Białkowski J.

1 Bocian R.

1 2004

1 2003

Wyniki wyszukiwania

On nonstandard tame selfinjective algebras having only periodic modules

The representation dimension of domestic weakly symmetric algebras