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: ecf227a73cf7c23610b586532efc2dceb43cfe03
Parent: 1261dc6376a8b86abc41efcfa3f7167c12b952f0
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 26 Sep 2022 17:53:10 +0000

Demoted a proposition to the mere status of a lemma

The proposition at hand is not interesting at all, it's simply an intermidiary step in the proof of the existence of the semisimplification of a coherent family

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
@@ -175,10 +175,10 @@
 % including it in here
 % TODO: Define the notation for M[mu] somewhere else
 % TODO: Note somewhere that M[mu] is a submodule
-\begin{proposition}
+\begin{lemma}
   Given a coherent family \(\mathcal{M}\) and \(\lambda \in \mathfrak{h}^*\),
   \(\mathcal{M}[\lambda]\) has finite length as a \(\mathfrak{g}\)-module.
-\end{proposition}
+\end{lemma}
 
 % TODO: Note that the semisimplification is only defined up to isomorphism: the
 % isomorphism class is independant of the composition series because all