by Bocian, R., Holm, T., Skowronski, A..

**Series:** 2003-35, Preprints

- MSC:
- 16D50 Injective modules, self-injective rings
- 16E10 Homological dimension
- 16G60 Representation type (finite, tame, wild, etc.)
- 18E30 Derived categories, triangulated categories

**Abstract:**

Auslander's representation dimension measures how

far a finite dimensional algebra is away from being of

finite representation type. 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 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.

**Keywords:**

representation dimension, weakly symmetric algebra, domestic representation type, derived equivalence