diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -727,8 +727,9 @@ century. Specifically, we find\dots
derivation \(C^\infty(G) \to C^\infty(G)\). All other \(G\)-invariant
differential operators are generated by invariant operators of order \(0\)
and \(1\). Hence \(\operatorname{Diff}(G)^G\) is generated by
- \(\operatorname{Der}(G)^G + K\) -- here \(\operatorname{Der}(G)^G \subset
- \operatorname{Der}(G)\) denotes the Lie subalgebra of invariant derivations.
+ \(\operatorname{Der}(G)^G + \mathbb{R}\) -- here \(\operatorname{Der}(G)^G
+ \subset \operatorname{Der}(G)\) denotes the Lie subalgebra of invariant
+ derivations.
Now recall that there is a canonical isomorphism of Lie algebras
\(\mathfrak{X}(G) \isoto \operatorname{Der}(G)\). This isomorphism takes left
@@ -751,8 +752,8 @@ century. Specifically, we find\dots
Since \(\mathcal{U}(\mathfrak{g})\) is generated by the image of the
inclusion \(\mathfrak{g} \to \mathcal{U}(\mathfrak{g})\), this implies \(\ker
\tilde f = 0\). Given that \(\operatorname{Diff}(G)^G\) is generated by
- \(\operatorname{Der}(G)^G + K\), this also goes to show \(\tilde f\) is
- surjective.
+ \(\operatorname{Der}(G)^G + \mathbb{R}\), this also goes to show \(\tilde f\)
+ is surjective.
\end{proof}
As one would expect, the same holds for complex Lie groups and algebraic groups