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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Representations of the generalized Kronecker quiver with countably many arrows


Author: Nils Mahrt
Journal: Proc. Amer. Math. Soc. 137 (2009), 815-824
MSC (2000): Primary 16G20; Secondary 16G70
Published electronically: September 10, 2008
MathSciNet review: 2457419
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Abstract: Let $ Q$ be the generalized Kronecker quiver with countably many arrows and let $ k$ be a field. We prove that the category of representations of $ Q$ over $ k$ has no right almost split morphism whose domain is projective. More precisely, we show that any indecomposable non-projective representation is the image of an epimorphism whose domain has no non-zero projective direct summand. This result does not hold for any finite subquiver of $ Q$.


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Additional Information

Nils Mahrt
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany
Email: nmahrt@math.uni-bielefeld.de

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09552-X
PII: S 0002-9939(08)09552-X
Keywords: Infinite generalized Kronecker quiver, almost split morphism
Received by editor(s): November 9, 2006
Received by editor(s) in revised form: May 23, 2007, August 31, 2007, December 20, 2007, and February 18, 2008
Published electronically: September 10, 2008
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.