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Geometry of the Moment Map for Representations of Quivers

Published online by Cambridge University Press:  04 December 2007

William Crawley-Boevey
William Crawley-Boevey
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, U.K. E-mail: w.crawley-boevey@leeds.ac.uk
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Abstract

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We study the moment map associated to the cotangent bundle of the space of representations of a quiver, determining when it is flat, and giving a stratification of its Marsden–Weinstein reductions. In order to do this we determine the possible dimension vectors of simple representations of deformed preprojective algebras. In an appendix we use deformed preprojective algebras to give a simple proof of much of Kac's Theorem on representations of quivers in characteristic zero.

Keywords

quiver representationmoment mappreprojective algebra
Type
Research Article
Information
Compositio Mathematica , Volume 126 , Issue 3 , May 2001 , pp. 257 - 293
Copyright
© 2001 Kluwer Academic Publishers