Noncommutative smoothness and coadjoint orbits

In [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 n(Q) of the corresponding quiver (Q) over right arrow. 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 etale 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. (C) 2002 Elsevier Science (USA). All rights reserved.