lie-algebras-and-their-representations

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -2249,7 +2249,7 @@ Moreover, we find\dots
   k_n \cdot \alpha_n\).
 
   This already gives us that the weights of \(M(\lambda)\) are bounded by
-  \(\lambda\) -- in the sence that no weight of \(M(\lambda)\) is ``higher''
+  \(\lambda\) -- in the sense that no weight of \(M(\lambda)\) is ``higher''
   than \(\lambda\). To see that \(\lambda\) is indeed a weight, we show that
   \(v^+\) is nonzero weight vector. Clearly \(v^+ \in V_\lambda\). The
   Poincaré-Birkhoff-Witt theorem implies
@@ -2387,7 +2387,7 @@ This last example is particularly interesting to us, since it indicates that
 the finite-dimensional irreducible representations of \(\mathfrak{sl}_2(K)\) as
 quotients of Verma modules. This is because the quotient
 \(\sfrac{M(\lambda)}{N(\lambda)}\) in example~\ref{ex:sl2-verma-quotient}
-happend to be finite-dimensional. As it turns out, this is always the case for
+happened to be finite-dimensional. As it turns out, this is always the case for
 semisimple \(\mathfrak{g}\). Namely\dots
 
 \begin{proposition}\label{thm:verma-is-finite-dim}