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Representations of the generalized Kronecker quiver with countably many arrows
Author(s):
Nils
Mahrt
Journal:
Proc. Amer. Math. Soc.
137
(2009),
815-824.
MSC (2000):
Primary 16G20;
Secondary 16G70
Posted:
September 10, 2008
MathSciNet review:
2457419
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Abstract:
Let  be the generalized Kronecker quiver with countably many arrows and let  be a field. We prove that the category of representations of  over  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  .
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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:
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
Posted:
September 10, 2008
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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