Lie algebraic characterization of manifolds
Lie algebraic characterization of manifolds
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流形的李代数表征
DOI：
10.2478/bf02475979
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发表时间：
2003
影响因子：
--
通讯作者：
N. Poncin
中科院分区：
文献类型：
--
作者：
J. Grabowski;N. Poncin
本文回顾和推广了用生长在流形上的某些李代数，特别是微分算子的李代数来刻画流形的结果。特别是，我们证明了一个光滑（实解析，斯坦）流形的特点是相应的李代数的线性微分算子，即同构的李代数诱导适当类的同胚的基础流形。
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operators, i.e. isomorphisms of such Lie algebras are induced by the appropriate class of diffeomorphisms of the underlying manifolds.