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An obstruction to quantizing compact symplectic manifolds. (English) Zbl 1097.53502

Summary: 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.

MSC:

53D50 Geometric quantization
17B63 Poisson algebras
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