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An obstruction to quantizing compact symplectic manifolds |
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| Authors: | Mark J. Gotay Janusz Grabowski Hendrik B. Grundling |
| Affiliation: | Department of Mathematics, University of Hawaii, 2565 The Mall, Honolulu, Hawaii 96822 ; Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland ; Department of Pure Mathematics, University of New South Wales, P.O. Box 1, Kensington, New South Wales, 2033 Australia |
| 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. |
| Keywords: | Symplectic manifolds quantization obstructions |
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