形式李群作用的线性性质
Finiteness properties of formal Lie group actions
摘要：
根据Arnold和Seigal-Yakovenko的思想，证明了形式李群作用的矩阵系数空间属于诺特环.利用这一结果，我们推广的一致交重数估计，这些作者从阿贝尔的情况下，一般李群。我们还证明了一个简单的新的证明喷确定结果Baouendi等。在本文的第二部分，我们使用类似的想法，证明了一个结果嵌入形式的单参数群的同态推广Takens的结果。特别是这意味着阿诺德和Seigal-Yakovenko的结果是正式的后果，我们的结果李群。
英文摘要：
Following ideas of Arnold and Seigal-Yakovenko, we prove that the space of matrix coefficients of a formal Lie group action belongs to a Noetherian ring. Using this result we extend the uniform intersection multiplicity estimates of these authors from the abelian case to general Lie groups. We also demonstrate a simple new proof for a jet-determination result of Baouendi et. al. In the second part of the paper we use similar ideas to prove a result on embedding formal diffeomorphisms in one-parameter groups extending a result of Takens. In particular this implies that the results of Arnold and Seigal-Yakovenko are formal consequence of our result for Lie groups.
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