Suppose that $G, H$ are Lie groups and $\mathfrak{g}$ the Lie algebra of $G$. Suppose that there is a Lie group action $G \times H \to H$. Is there a natural $\mathfrak{g}$ action on $C^{\infty}(H)$? Thank you very much.
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asked Feb 25, 2018 at 11:08
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4$\begingroup$ Yes, by the vector fields of the associated Lie algebra action on $H$. $\endgroup$– Ben McKayCommented Feb 25, 2018 at 11:21
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