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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Indecomposables live in all smaller lengths
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by Klaus Bongartz
Represent. Theory 17 (2013), 199-225
Published electronically: April 5, 2013


We show that there are no gaps in the lengths of the indecomposable objects in an abelian $k$-linear category over a field $k$ provided all simples are absolutely simple. To derive this natural result we prove that any distributive minimal representation-infinite $k$-category is isomorphic to the linearization of the associated ray category which is shown to have an interval-finite universal cover with a free fundamental group so that the well-known theory of representation-finite algebras applies.
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Bibliographic Information
  • Klaus Bongartz
  • Affiliation: Universität Wuppertal, Germany
  • Email:
  • Received by editor(s): March 9, 2012
  • Received by editor(s) in revised form: October 15, 2012
  • Published electronically: April 5, 2013

  • Dedicated: Dedicated to A. V. Roiter and P. Gabriel
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 17 (2013), 199-225
  • MSC (2010): Primary 16G10, 16G20, 20C05
  • DOI:
  • MathSciNet review: 3038490