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Mathematische Zeitschrift

, Volume 240, Issue 1, pp 141–167 | Cite as

Necklace Lie algebras and noncommutative symplectic geometry

  • Raf Bocklandt
  • Lieven Le Bruyn
Original article

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.

Keywords

Phase Space Symplectic Geometry Coadjoint Orbit Combinatorial Description Relevant Couple 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Raf Bocklandt
    • 1
  • Lieven Le Bruyn
    • 1
  1. 1.Universiteit Antwerpen (UIA), B-2610 Antwerp, Belgium (e-mail: rbockl@wins.uia.ac.be; http://win-www.uia.ac.be/u/rbockl/; lebruyn@wins.uia.ac.be; http://win-www.uia.ac.be/u/lebruyn/) BE

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