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On minimal disjoint degenerations for preprojective representations of quivers

Authors: Klaus Bongartz and Thomas Fritzsche
Journal: Math. Comp. 72 (2003), 2013-2042
MSC (2000): Primary 16G20, 14L30
Published electronically: February 3, 2003
MathSciNet review: 1986819
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Abstract: We derive a root test for degenerations as described in the title. In the case of Dynkin quivers this leads to a conceptual proof of the fact that the codimension of a minimal disjoint degeneration is always one. For Euclidean quivers, it enables us to show a periodic behaviour. This reduces the classification of all these degenerations to a finite problem that we have solved with the aid of a computer. It turns out that the codimensions are bounded by two. Somewhat surprisingly, the regular and preinjective modules play an essential role in our proofs.

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Additional Information

Klaus Bongartz
Affiliation: FB Mathematik BUGH Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany

Thomas Fritzsche
Affiliation: FB Mathematik BUGH Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany

Received by editor(s): March 1, 2001
Received by editor(s) in revised form: March 4, 2002
Published electronically: February 3, 2003
Article copyright: © Copyright 2003 American Mathematical Society