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Infinite Length Modules

  • Henning Krause
  • Claus Michael Ringel

Part of the Trends in Mathematics book series (TM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. K. I. Pimenov, A. V. Yakovlev
    Pages 101-105
  3. T. H. Lenagan
    Pages 129-147
  4. Alex Martsinkovsky
    Pages 167-192
  5. Aidan Schofield
    Pages 297-309
  6. Grzegorz Zwara
    Pages 311-319
  7. Raymundo Bautista
    Pages 321-330

About these proceedings

Introduction

This volume presents the invited lectures of a conference devoted to Infinite Length Modules, held at Bielefeld, September 7-11, 1998. Some additional surveys have been included in order to establish a unified picture. The scientific organization of the conference was in the hands of K. Brown (Glasgow), P. M. Cohn (London), I. Reiten (Trondheim) and C. M. Ringel (Bielefeld). The conference was concerned with the role played by modules of infinite length when dealing with problems in the representation theory of algebras. The investi­ gation of such modules always relies on information concerning modules of finite length, for example simple modules and their possible extensions. But the converse is also true: recent developments in representation theory indicate that a full un­ derstanding of the category of finite dimensional modules, even over a finite dimen­ sional algebra, requires consideration of infinite dimensional, thus infinite length, modules. For instance, the important notion of tameness uses one-parameter fami­ lies of modules, or, alternatively, generic modules and they are of infinite length. If one tries to exhibit a presentation of a module category, it turns out to be essential to take into account the indecomposable modules which are algebraically compact, or, equivalently, pure injective. Specific methods have been developed over the last few years dealing with such special situations as group algebras of finite groups or noetherian rings, and there are surprising relations to topology and geometry. The conference outlined the present state of the art.

Keywords

Finite Microsoft Access Volume addition algebra cohomology compactness development finite group homology knowledge matrix representation theory ring topology

Editors and affiliations

  • Henning Krause
    • 1
  • Claus Michael Ringel
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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