lie-algebras-and-their-representations

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -34,14 +34,14 @@ The fundamental difference between these two cases is thus the fact that \(\dim
 question then is: why did we choose \(\mathfrak{h}\) with \(\dim \mathfrak{h} >
 1\) for \(\mathfrak{sl}_3(K)\)?
 
-The rational behind fixing an Abelian subalgebra is a simple one: we have seen
-in the previous chapter that representations of Abelian algebras are generally
-much simpler to understand than the general case. Thus it make sense to
-decompose a given representation \(V\) of \(\mathfrak{g}\) into subspaces
-invariant under the action of \(\mathfrak{h}\), and then analyze how the
-remaining elements of \(\mathfrak{g}\) act on this subspaces. The bigger
-\(\mathfrak{h}\) is, the simpler our problem gets, because there are fewer
-elements outside of \(\mathfrak{h}\) left to analyze.
+The rational behind fixing an Abelian subalgebra \(\mathfrak{h}\) is a simple
+one: we have seen in the previous chapter that representations of Abelian
+algebras are generally much simpler to understand than the general case. Thus
+it make sense to decompose a given representation \(V\) of \(\mathfrak{g}\)
+into subspaces invariant under the action of \(\mathfrak{h}\), and then analyze
+how the remaining elements of \(\mathfrak{g}\) act on this subspaces. The
+bigger \(\mathfrak{h}\) is, the simpler our problem gets, because there are
+fewer elements outside of \(\mathfrak{h}\) left to analyze.
 
 Hence we are generally interested in maximal Abelian subalgebras \(\mathfrak{h}
 \subset \mathfrak{g}\), which leads us to the following definition.