The theme

If one deals with artin algebras and their module categories one feels that those of finite global dimension seem to be the most accessible ones. Indeed, artin algebras of global dimension at most 1, the hereditary algebras, are quite well understood. However, aready for global dimension 2, one gets stuck: one knows a lot of examples (but they are not yet sorted), and one observes that there are algebras with quite different behaviour: of course, there are the tilted algebras and the quasi-hereditary algebras of global dimension 2, but they seem to be well-behaved. In general one may look at the tensor algebra of the A-A-bimodule Ext2(DA,A), note that this algebra may be infinite dimensional even for quasi-hereditary algebras. Looking at various conjectures in the representation theory of artin algebras, it turns out that many are not settled even in the case of projective dimension 2.

The workshop is devoted to the presentation of examples of the strange behaviour of some artin algebras of global dimension 2, to general problems where already the restriction to dimension 2 is open, and to proposals how a structure theory of these artin algebras and their module categories may look like.

The present schedule includes an overview on the difficulties of projective dimension 2 by Dieter Happel, and lectures by Idun Reiten, Steffen Oppermann, Winfried Bruns, Sefi Ladkani, and Helmut Lenzing.

Anyone interested in the subject is invited to participate. Short (or longer) contributions are very well-come, please contact C.M.Ringel ( Financial support can be provided by the CRC 701, Bielefeld, please contact C.M.Ringel (

If you like to participate, we would appreciate that you send a short message to Please indicate whether you will join the dinner.

The aim of the workshop is to collect (and make available) as much information and questions as possible.

Anyone is invited to provide suitable material on the topic, in the same way as it was done at several previous Bielefeld workshops.

Since the workshop has been announced on a very short notice, we cannot expect too many visitors from abroad, thus there is been the proposal that it may be used as a preparation for a slightly larger meeting early next year (either in Bielefeld or as part of the Bonn activities).