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Derived equivalence classification of weakly symmetric algebras of domestic type

Rafał BocianAndrzej Skowroński — 2016

Colloquium Mathematicae

We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.

The representation dimension of domestic weakly symmetric algebras

Rafał BocianThorsten HolmAndrzej Skowroński — 2004

Open Mathematics

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...

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