半单李代数的单纯作用

On Simple Actions of Semisimple Lie Algebras

本文证明了任何半单李代数(或者李群)在连通光滑流形上的非平凡单纯作用一定没有驻点．而且有效作用的那部分必定是同构于sl(2,R)(或者SL(2,R))的理想．

This paper proves that, for any semisimple Lie algebra （or Lie group）, its simple action on a connected smooth manifold cannot have stationary points. Moreover, the effective part of this action merely comes from an ideal isomorphic to sl（2,R） （or SL（2, R））.