Gelfand-Kirillov conjecture for symplectic reflection algebras

Details Gelfand-Kirillov conjecture for symplectic reflection algebras Gelfand-Kirillov conjecture for symplectic reflection algebras

2007-10-07

arxiv.org/abs/0710.1419v3

Mathematics

Rings and Algebras

The generators and relations given in 2.4 are not correct. Specifically the commutation relation (3) needs to be changed. I do

Scientific paper

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.

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