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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

Published online by Cambridge University Press:  12 January 2010

K. A. Brown  and
K. Changtong
K. A. Brown
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK, Email: ([email protected])
K. Changtong
Affiliation:
Department of Mathematics, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand, Email: ([email protected])
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Abstract

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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.

Keywords

symplectic reflection algebrarational Cherednik algebrafields of positive characteristic

MSC classification

Secondary: 16S99: None of the above, but in this section 16G30: Representations of orders, lattices, algebras over commutative rings
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 61 - 81
Copyright
Copyright © Edinburgh Mathematical Society 2010