Let $G$ be a Lie group with identity element $e$, [Lie algebra](/page/Lie%20Algebra) $\mathfrak g=T_eG$, and let $N\trianglelefteq G$ be a closed normal Lie subgroup with Lie algebra $\mathfrak n=T_eN$. Suppose that the [quotient group](/theorems/790) $G/N$ is equipped with its standard quotient Lie group structure, and let $eN\in G/N$ denote its identity coset. Then $\mathfrak n$ is an ideal in $\mathfrak g$, and there is a natural Lie algebra isomorphism

\begin{align*} \mathfrak g/\mathfrak n \cong \operatorname{Lie}(G/N)=T_{eN}(G/N). \end{align*}