Title 



Necklace Lie algebras and noncommutative symplectic geometry


Author 





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. CrawleyBoevey 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.  

Language 



English


Source (journal) 



Mathematische Zeitschrift.  Berlin 

Publication 



Berlin : 2002


ISSN 



00255874


Volume/pages 



240:1(2002), p. 141167


ISI 



000176302300008


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