Noncommutative smoothness and coadjoint orbits

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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 NQof the corresponding quiver Q. 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. © 2002 Elsevier Science (USA). All rights reserved.




Le Bruyn, L. (2002). Noncommutative smoothness and coadjoint orbits. Journal of Algebra, 258(1), 60–70.

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