Abstract
Let Andenote the Weyl algebra of all differential operators on the polynomial algebra C[X1,… Xn].It is well known that if G is a finite group of algebra automorphisms of An, then An is a simple algebra. (See [12] pp. 20–23 for an algebraic proof or [15] Lemma 1.2 for an analytic approach.) It is natural to expect that the analogous result holds for the associated graded object. To be precise, if Anis filtered by total degree, then the associated graded algebra is the larger polynomial ring R = C[X1, …Xn,Y1,… Yn]with the Poisson bracket which describes a standard symplectic affine space. To be explicit R is also a Lie algebra subject to
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Dedicated to A. A. Kirillov on the occasion of his 65th birthday
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Alev, J., Farkas, D.R. (2003). Finite Group Actions on Poisson Algebras. In: Duval, C., Ovsienko, V., Guieu, L. (eds) The Orbit Method in Geometry and Physics. Progress in Mathematics, vol 213. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0029-1_2
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DOI: https://doi.org/10.1007/978-1-4612-0029-1_2
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