30th-siicusp

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}