##  [Lie Group Action](/index.php/lie-group-action) 

  ##  [Lie Group Action](https://natural.quantumdictionary.io/lie-group-action-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A smooth map describing how elements of a Lie group act as smooth transformations on a differentiable manifold, i.e., a group homomorphism from the Lie group into the group of diffeomorphisms of the manifold that is smooth in both group element and base point.