Approximating finite dimensional representations by infinite dimensional ones
by
Birge Huisgen-Zimmermann
University of California at Santa Barbara

My talk (based on work with Dieter Happel and an ongoing collaboration with Sverre Smalø) will start out with a functorial finiteness condition for module categories over Artin algebras which was introduced by Auslander and Smalø in 1970; namely, contravariant finiteness. A few years ago, contravariant finiteness of the category C of finitely generated modules of finite projective dimension was shown to entail deep homological consequences for the underlying algebra. The more recent results at which I will aim here address the following two goals: first, that of testing contravariant finiteness by exhibiting certain modules which are infinite dimensional if and only if C fails to be contravariantly finite - they can often be constructed explicitly from quiver and relations; secondly, to illustrate the amount of information stored in these modules beyond their capacity to serve as indicators in the mentioned test.

Date received: January 9, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-49.