Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Representation Theory
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 16G10, 16G20, 20C05

Retrieve articles in all journals with MSC (2010): 16G10, 16G20, 20C05


Additional Information

Klaus Bongartz
Affiliation: Universität Wuppertal, Germany
Email: bongartz@math.uni-wuppertal.de

DOI: http://dx.doi.org/10.1090/S1088-4165-2013-00429-6
PII: S 1088-4165(2013)00429-6
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.