lie-algebras-and-their-representations

Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules

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1 file changed, 7 insertions, 0 deletions

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -344,6 +344,13 @@ also share structural features with groups. For example\dots
   Abelian.
 \end{example}
 
+\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 \(\mathfrak{z}\)}.
+\end{example}
+
 \begin{definition}
   A Lie algebra \(\mathfrak{g}\) is called \emph{solvable} if its derived
   series