diff --git a/main.tex b/main.tex
@@ -116,10 +116,10 @@
\begin{definition}
A álgebra de Lie \(\mathfrak{g} = \operatorname{Lie}(G)\) é a
\(\mathbb{R}\)-álgebra de Lie dos campos \(X \in \mathfrak{X}(G)\) tais que
- \(X_g = (d \ell_g)_1 X_1 \, \forall g \in G\), com
+ \(X_g = (d \ell_g)_e X_e \, \forall g \in G\), com
\begin{gather*}
[X, Y] f = X Y f - Y X f \\
- X, Y \in \mathfrak{g} \quad f \in C^\infty(G)
+ X, Y \in \mathfrak{g}, \quad f \in C^\infty(G)
\end{gather*}
\end{definition}
\begin{itemize}