University of Sydney
School of Mathematics and Statistics
Beijing Normal University
The representation dimension of algebras.
Wednesday 13th December, 10-11am, Carslaw 275.
Given a finite dimensional algebra A over a field,
Auslander defined in 1971 the representation dimension of A
to be the minimum of the global dimensions of the endomorphism
algebras of generator-cogenerators of the A-module
category. It was shown that an algebra is of representation-finite
type if and only if the representation dimension is at most
2. However, it is still open whether the representation
dimension of an algebra is finite or not. In this talk, we shall
show that if there is a stable equivalence of Morita-type between
two algebras A and B, then they have the same
representation dimension. So representation dimension is an
invariant of stable equivalence of Morita-type (but note that it is
not an invariant of derived equivalences).