Introduction

Summary

The Tsukuba International Conference on Representations of Algebras and Related Topics(1) took place in the week before the International Congress of Mathematicians in Kyoto (1990). The Conference was preceded by a Workshop in which leading workers in the field gave expository lectures on recent developments in areas covered by the Conference.

The aim of this book is to present the Workshop lectures to a wider audience. The participants at the Workshop were not all specialists in the area and so the speakers aimed to make their talks as self-contained as possible. This is reflected in their papers presented here. Several of the authors have taken the opportunity to update their manuscripts, most of which contain results which have not appeared elsewhere. We have included one paper (Dlab's) which was not presented at the Workshop.

The Tsukuba meetings took place at a time of exciting and highly complex interaction between the representation theory of algebras and other branches of mathematics. Several of the powerful technologies developed within algebra representation theory during its rather introspective period from about 1970 to the mid–1980s are now contributing strongly to other areas. In the opposite direction, new problems, ideas and points of view are coming into the subject from previously unrelated areas. Some of these interactions are reflected in the present volume.

The study of functor categories (categories of abelian group valued functors on module categories) is one of the most successful methodologies of algebra representation theory and underlies key concepts like those of almost split sequence and Auslander-Reiten quiver.