Gotay, Mark J.; Grabowski, Janusz; Grundling, Hendrik B. An obstruction to quantizing compact symplectic manifolds. (English) Zbl 1097.53502 Proc. Am. Math. Soc. 128, No. 1, 237-243 (2000). 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. Cited in 4 Documents MSC: 53D50 Geometric quantization 17B63 Poisson algebras Keywords:Symplectic manifolds; quantization; obstructions PDFBibTeX XMLCite \textit{M. J. Gotay} et al., Proc. Am. Math. Soc. 128, No. 1, 237--243 (2000; Zbl 1097.53502) Full Text: DOI arXiv