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.
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机译：结果表明，光滑的泊松空间可能与有限生成的泊松 R -代数有关。展示了有限生成的泊松 R -代数（ A ，π），其相关的光滑泊松空间可能未嵌入任何尺寸为12或更小的泊松流形中，平滑空间可以嵌入 R 11 中。证明不断打开，表明从12个变量的形式幂级数Poisson代数到最大理想（ A ，π）的完成都没有排斥。
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