Let $G$ be a Lie group with identity element $e$, and let $\mathfrak g:=T_eG$ be its [Lie algebra](/page/Lie%20Algebra). Let $V$ be a finite-dimensional real or complex [vector space](/page/Vector%20Space), and let
paragraph
admin
\begin{align*}
\rho:G\to GL(V)
\end{align*}
latex_env
admin
be a smooth finite-dimensional representation of $G$. Define the differentiated representation