Necklace Lie algebras and noncommutative symplectic geometry
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Recently, V. Ginzburg proved that Calogero phase space is a coadjoint orbit for some infinite dimensional Lie algebra coming from noncommutative symplectic geometry, . 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 . Using results of W. Crawley-Boevey and M. Holland ,  and  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.
KeywordsPhase Space Symplectic Geometry Coadjoint Orbit Combinatorial Description Relevant Couple
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