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Representation Theory

ISSN 1088-4165



Indecomposables live in all smaller lengths

Author: Klaus Bongartz
Journal: Represent. Theory 17 (2013), 199-225
MSC (2010): Primary 16G10, 16G20, 20C05
Published electronically: April 5, 2013
MathSciNet review: 3038490
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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

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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.