We construct functorially a class of algebras using the formalism of double derivations. These algebras extend to higher dimensions Crawley-Boevey 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.
- Pub Date:
- October 2007
- Mathematics - Rings and Algebras;
- Mathematics - Representation Theory
- 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