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