diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -369,15 +369,15 @@ There is also a natural analogue of quotients.
any linear map \(\mathfrak{g} \to \mathfrak{h}\) between Abelian Lie algebras
\(\mathfrak{g}\) and \(\mathfrak{h}\) is a homomorphism of Lie algebras. In
particular, any linear isomorphism \(\mathfrak{g} \isoto K^n\) -- where
- \(K^n\) is endowed with the trivial bracket \([v, w] = 0 \, \forall v, w \in
- K^n\) -- is an isomorphism of Lie algebras for Abelian \(\mathfrak{g}\).
+ \(K^n\) is endowed with the trivial bracket \([v, w] = 0\), \(v, w \in K^n\)
+ -- is an isomorphism of Lie algebras for Abelian \(\mathfrak{g}\).
\end{note}
\begin{example}
Let \(\mathfrak{g}\) be a Lie algebra and \(\mathfrak{z} = \{ X \in
- \mathfrak{g} : [X, Y] = 0 \; \forall Y \in \mathfrak{g}\}\). Then
- \(\mathfrak{z}\) is an Abelian ideal of \(\mathfrak{g}\), known as \emph{the
- center of \(\mathfrak{z}\)}.
+ \mathfrak{g} : [X, Y] = 0, Y \in \mathfrak{g}\}\). Then \(\mathfrak{z}\) is
+ an Abelian ideal of \(\mathfrak{g}\), known as \emph{the center of
+ \(\mathfrak{z}\)}.
\end{example}
Due to their relationship with Lie groups and algebraic groups, Lie algebras