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2003-35

The representation dimension of domestic weakly symmetric algebras

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