lie-algebras-and-their-representations

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -1904,7 +1904,6 @@ Jordan decomposition of a semisimple Lie algebra}.
   The pair \((T_s, T_n)\) is known as \emph{the Jordan decomposition of \(T\)}.
 \end{proposition}
 
-% TODOO: Prove this? It suffices to show that ad(X)_s, ad(X)_n in ad(g)!
 \begin{proposition}
   Given \(\mathfrak{g}\) semisimple and \(X \in \mathfrak{g}\), there are
   \(X_s, X_n \in \mathfrak{g}\) such that \(X = X_s + X_n\), \([X_s, X_n] =
@@ -2124,7 +2123,7 @@ then\dots
   all congruent module the root lattice \(Q = \ZZ \Delta\) of \(\mathfrak{g}\).
 \end{theorem}
 
-% TODO: Turn this into a proper discussion of basis and give the idea of the
+% TODOO: Turn this into a proper discussion of basis and give the idea of the
 % proof of existance of basis?
 To proceed further, as in the case of \(\mathfrak{sl}_3(K)\) we have to fix a
 direction in \(\mathfrak{h}^*\) -- i.e. we fix a linear function
@@ -2147,7 +2146,7 @@ roots of \(\mathfrak{g}\) and once more we find\dots
 % TODO: Here we may take a weight of maximal height, but why is it unique?
 % TODO: We don't really need to talk about height tho, we may simply take a
 % weight that maximizes B(gamma, lambda) in QQ
-% TODO: Either way, we need to move this to after the discussion on the
+% TODOO: Either way, we need to move this to after the discussion on the
 % integrality of weights
 \begin{proof}
   It suffices to note that if \(\lambda\) is the weight of \(V\) lying the