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symplectic reflection algebra

Proceedings of the Edinburgh Mathematical Society (1)

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Symplectic reflection algebras in positive characteristic
Part of
- Rings and algebras arising under various constructions
- Representation theory of rings and algebras
K. A. Brown, K. Changtong
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 1 / February 2010

Published online by Cambridge University Press:

12 January 2010, pp. 61-81
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Basic properties of symplectic reflection algebras over an algebraically closed field k of positive characteristic are laid out. These algebras are always finite modules over their centres, in contrast to the situation in characteristic 0. For the subclass of rational Cherednik algebras, we determine the PI-degree and the Goldie rank, and show that the Azumaya and smooth loci of the centre coincide.