Abstract.
Recently, V. Ginzburg proved that Calogero phase space is a coadjoint orbit for some infinite dimensional Lie algebra coming from noncommutative symplectic geometry, [12]. In this note we generalize his argument to specific quotient varieties of representations of (deformed) preprojective algebras. This result was also obtained independently by V. Ginzburg [13]. Using results of W. Crawley-Boevey and M. Holland [10], [8] and [9] we give a combinatorial description of all the relevant couples \((\alpha,\lambda)\) which are coadjoint orbits. We give a conjectural explanation for this coadjoint orbit result and relate it to different noncommutative notions of smoothness.
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Received: 19 October 2000; in final form: 9 May 2001 / Published online: 28 February 2002
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Bocklandt, R., Le Bruyn, L. Necklace Lie algebras and noncommutative symplectic geometry. Math Z 240, 141–167 (2002). https://doi.org/10.1007/s002090100366
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DOI: https://doi.org/10.1007/s002090100366