lie-algebras-and-their-representations

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -1156,7 +1156,7 @@ automorphisms \(\varphi_\lambda : \operatorname{Diff}(K[x, x^{-1}]) \to
 \(\mathcal{U}(\mathfrak{sl}_2(K))\) via the map
 \(\mathcal{U}(\mathfrak{sl}_2(K)) \to \operatorname{Diff}(K[x, x^{-1}])\), but
 we could just as well twist \(K[x, x^{-1}]\) by automorphisms of
-\(\mathcal{U}(\mathfrak{sl}_2(K))_f\) -- where
+\(\mathcal{U}(\mathfrak{sl}_2(K))_f\) directly -- where
 \(\mathcal{U}(\mathfrak{sl}_2(K))_f\) denotes the localization of
 \(\mathcal{U}(\mathfrak{sl}_2(K))\) by the multiplicative subset generated by
 \(f\). In fact, \(\varphi_\lambda\) factors trought an automorphism