lie-algebras-and-their-representations

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -676,8 +676,8 @@ The structure of \(\mathcal{U}(\mathfrak{g})\) can often be described in terms
 of the structure of \(\mathfrak{g}\). For instance, \(\mathfrak{g}\) is Abelian
 if, and only if \(\mathcal{U}(\mathfrak{g})\) is commutative, in which case any
 basis \(\{X_i\}_i\) for \(\mathfrak{g}\) induces an isomorphism
-\(\mathcal{U}(\mathfrak{g}) \cong K[X_1, \ldots, X_i, \ldots]\). More generally,
-we find\dots
+\(\mathcal{U}(\mathfrak{g}) \cong K[x_1, x_2, \ldots, x_i, \ldots]\). More
+generally, we find\dots
 
 \begin{theorem}[Poincaré-Birkoff-Witt]\index{PBW Theorem}
   Let \(\mathfrak{g}\) be a Lie algebra over \(K\) and \(\{X_i\}_i \subset