Title
Noncommutative smoothness and coadjoint orbits Noncommutative smoothness and coadjoint orbits
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Journal of algebra. - New York, N.Y.
Volume/pages
258(2002) :1 , p. 60-70
ISSN
0021-8693
ISI
000179972900003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In [math.AG/0010030; Math. Z., to appear] R. Bocklandt and the author proved that certain quotient varieties of representations of deformed preprojective algebras are coadjoint orbits for the necklace Lie algebra n(Q) of the corresponding quiver (Q) over right arrow. A conjectural ring.-theoretical explanation of these results was given in terms of noncommutative smoothness in the sense of C. Procesi [J. Algebra 107 (1987) 63-74]. In this paper we prove these conjectures. The main tool in the proof is the etale local description due to W. Crawley-Boevey [math. AG/0105247]. Along the way we determine the smooth locus of the Marsden-Weinstein reductions for quiver representations. (C) 2002 Elsevier Science (USA). All rights reserved.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/eed4ea/3140.pdf
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