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

git clone: git://git.pablopie.xyz/lie-algebras-and-their-representations
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Commit: 8f196d3fd742bb18debcbb8f76eebc05e7a01faf
Parent: 7346488bf450127872b09f2236480ee50f256421
Author: Pablo <pablo-escobar@riseup.net>
Date: Sat, 19 Nov 2022 20:23:48 +0000

Added the center of a Lie algebra to the list of examples of Abelian algebras

Diffstat

1 file changed, 7 insertions, 0 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	7	7	0

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