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An obstruction to quantizing
compact symplectic manifolds

Authors: Mark J. Gotay, Janusz Grabowski and Hendrik B. Grundling
Journal: Proc. Amer. Math. Soc. 128 (2000), 237-243
MSC (1991): Primary 81S99; Secondary 17B66
Published electronically: May 20, 1999
MathSciNet review: 1622742
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Abstract: We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the existence of a universal obstruction to quantizing a compact symplectic manifold, regardless of the dimensionality of the representation.

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Additional Information

Mark J. Gotay
Affiliation: Department of Mathematics, University of Hawaii, 2565 The Mall, Honolulu, Hawaii 96822

Janusz Grabowski
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

Hendrik B. Grundling
Affiliation: Department of Pure Mathematics, University of New South Wales, P.O. Box 1, Kensington, New South Wales, 2033 Australia

Keywords: Symplectic manifolds, quantization, obstructions
Received by editor(s): March 11, 1998
Published electronically: May 20, 1999
Communicated by: Peter Li
Article copyright: © Copyright 1999 American Mathematical Society