03-35
The representation dimension of domestic weakly symmetric algebras
by Bocian, R.; Holm, T.; Skowronski, A.
Preprint series: 03-35, Preprints
- MSC:
- 16D50 Injective modules, self-injective rings, See also {16L60, 18G05}
- 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
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