Noncommutative Symplectic Geometry
by
Ken Brown
University of Glasgow

I will describe a large class of (noncommutative noetherian) algebras introduced and studied in a recent preprint of P. Etinghof and V. Ginzburg, (AG/0011114). These algebras are deformations of skew group algebras of finite groups acting on polynomial algebras. They include as special cases skew group algebras over the Weyl algebras and the deformations of Kleinian singularities studied by Crawley-Boevey and Holland (Duke Math. J. 1998). They are expected to have important applications, for example to differential operators, representation theory of Hecke algebras and to symplectic resolution of singularities. Being rather straightforward to define but having nevertheless an extremely rich and beautiful structure, these algebras illustrate in a rather transparent way some of the major themes which are emerging in the subject beginning to be known as "non-commutative algebraic geometry". I'll describe new results of myself and Iain Gordon on the structure of these "symplectic reflection algebras".

Paper reference: arXiv:math.RT/0201042

Date received: February 23, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cage-06.