GelfandKirillov conjecture for symplectic reflection algebras
Abstract
We construct functorially a class of algebras using the formalism of double derivations. These algebras extend to higher dimensions CrawleyBoevey and Holland's construction of deformed preprojective algebras and encompass symplectic reflection algebras associated to wreath products. We use this construction to show that the quotient field of a symplectic reflection algebra is "rational", confirming a pair of conjectures of Etingof and Ginzburg.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1419
 Bibcode:
 2007arXiv0710.1419G
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Representation Theory
 EPrint:
 The generators and relations given in 2.4 are not correct. Specifically the commutation relation (3) needs to be changed. I do not know how to do this in general, and so the preprint is incorrect as it stands. Corollary 6.3 is correct, however, and is used in arXiv:0709.2338