| It is shown that smooth Poisson spaces may be associated to finitely generated Poisson R-algebras. A finitely generated Poisson R-algebra (A, π) is exhibited whose associated smooth Poisson space may not be embedded into any Poisson manifold of dimension 12 or less, although the underlying smooth space may be embedded into R11. The proof turns on showing that there is no surjection from a formal power series Poisson algebra in 12 variables to a completion of (A, π) at a maximal ideal. |
