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: e498f776d2b61fd00a05f1b994fbfa3bf3e2c7ee
Parent: 23770f04ed7d493e5fbdfd859e0559b7da99eaea
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 16 Oct 2022 14:47:44 +0000

Minor correction

Diffstat

1 file changed, 2 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	4	2	2

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -374,8 +374,8 @@
   \(K\)-linear operator \(\mathcal{M}_\lambda \to \mathcal{M}_\lambda\), so
   that \(W = 0\) or \(W = \mathcal{M}_\lambda\).
 
-  On the other hand, if \(\mathcal{M}_\lambda\) is simple then by Jacobson's
-  density theorem the map \(\mathcal{U}(\mathfrak{g})_0 \to
+  On the other hand, if \(\mathcal{M}_\lambda\) is simple then by Burnside's
+  theorem on matrix algebras the map \(\mathcal{U}(\mathfrak{g})_0 \to
   \operatorname{End}(\mathcal{M}_\lambda)\) is surjective. Hence the
   commutativity of the previously drawn diagram, as well as the fact that
   \(\operatorname{rank}(\mathcal{U}(\mathfrak{g})_0 \to