lie-algebras-and-their-representations

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -552,10 +552,10 @@
   \operatorname{Diff}(G)^G\) -- here \(\operatorname{Der}(G)^G \subset
   \operatorname{Der}(G)\) denotes the Lie subalgebra of invariant derivations.
 
-  Since \(f\) is a homomorphism of Lie algebras, it extends to an algebra
-  homomorphism \(g : \mathcal{U}(\mathfrak{g}) \to \operatorname{Diff}(G)^G\).
-  We claim \(g\) is an isomorphim. To see that \(g\) is injective, it suffices
-  to notice
+  Since \(f\) is a homomorphism of Lie algebras, it can be extended to an
+  algebra homomorphism \(g : \mathcal{U}(\mathfrak{g}) \to
+  \operatorname{Diff}(G)^G\). We claim \(g\) is an isomorphim. To see that
+  \(g\) is injective, it suffices to notice
   \[
     g(X_1 \cdots X_n)
     = g(X_1) \cdots g(X_n)