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Title
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Necklace Lie algebras and noncommutative symplectic geometry
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Author
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Abstract
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| Recently, V. Ginzburg proved that Calogero phase space is a coadjoint orbit for some infinite dimensional Lie algebra coming from non-commutative 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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Language
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English
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Source (journal)
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Mathematische Zeitschrift. - Berlin, 1918, currens
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Publication
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Berlin
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2002
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ISSN
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0025-5874
[print]
1432-1823
[online]
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DOI
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10.1007/S002090100366
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Volume/pages
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240
:1
(2002)
, p. 141-167
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ISI
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000176302300008
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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