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: 41f8550180ad1a8646b52cf4c81c4b173462c14f
Parent: d0cbf9ca62547857bfa820c7ae70ad7f4de098ff
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 2 Jan 2023 17:51:06 +0000

Demoted a theorem to a proposition

Diffstat

1 file changed, 2 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	4	2	2

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -940,11 +940,11 @@ This sequence always splits, which implies we can deduce information about
 part'' \(\mfrac{\mathfrak{g}}{\mathfrak{rad}(\mathfrak{g})}\) -- see
 Proposition~\ref{thm:quotients-by-rads}. In practice this translates to\dots
 
-\begin{theorem}\label{thm:semi-simple-part-decomposition}
+\begin{proposition}
   Every simple \(\mathfrak{g}\)-module is the tensor product of
   a simple \(\mfrac{\mathfrak{g}}{\mathfrak{rad}(\mathfrak{g})}\)-module 
   and a \(1\)-dimensional \(\mathfrak{rad}(\mathfrak{g})\)-module.
-\end{theorem}
+\end{proposition}
 
 Having finally reduced our initial classification problem to that of
 classifying the finite-dimensional simple \(\mathfrak{g}\)-modules, we can now