Answer by Jack Lee for Identification of the Lie algebra of an isotropy group...
The hypothesis of the statement is that $G$ acts transitively on $M$, meaning that for any $p,q\in M$ there exists $g\in G$ such that $g\centerdot p=q$. In your example, $S^1$ does not act transitively...
View ArticleIdentification of the Lie algebra of an isotropy group with the tangent space...
I think I am stuck with the following statement that I read on the Encyclopedia of Mathematics website regarding Isotropy representations:"If $G$ is a Lie group acting smoothly and transitively on $M$...
View Article
More Pages to Explore .....
