Noncommutative smoothness and coadjoint orbits

n [math.AG/0010030; Math. Z., to appear] R. Bocklandt and the author proved that certain quotient varieties of representations of deformed preprojective algebras are coadjoint orbits for the necklace Lie algebra of the corresponding quiver . A conjectural ring-theoretical explanation of these results was given in terms of noncommutative smoothness in the sense of C. Procesi [J. Algebra 107 (1987) 63–74]. In this paper we prove these conjectures. The main tool in the proof is the étale local description due to W. Crawley-Boevey [math.AG/0105247]. Along the way we determine the smooth locus of the Marsden–Weinstein reductions for quiver representations.