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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Indecomposables live in all smaller lengths
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by Klaus Bongartz PDF
Represent. Theory 17 (2013), 199-225 Request permission

Abstract:

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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Additional Information
  • Klaus Bongartz
  • Affiliation: Universität Wuppertal, Germany
  • Email: bongartz@math.uni-wuppertal.de
  • 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: https://doi.org/10.1090/S1088-4165-2013-00429-6
  • MathSciNet review: 3038490