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
Log
Files
Refs
README
LICENSE

Commit: 6b76e44e70922a10e47a2f37fb78f1a709bb829f
Parent: 9bbab87c16919043a2db660c996645b7bbfd745e
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 29 May 2023 13:30:48 +0000

Removed duplicate labels

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
@@ -125,7 +125,7 @@ In case the relationship between complete reducibility, semisimplicity of
 \(\mathfrak{g}\)-modules and the simplicity of indecomposable modules is
 unclear, the following results should clear things up.
 
-\begin{proposition}\label{thm:complete-reducibility-equiv}
+\begin{proposition}
   The following conditions are equivalent.
   \begin{enumerate}
     \item Every submodule of a finite-dimensional \(\mathfrak{g}\)-module is
@@ -256,7 +256,7 @@ We are now ready to answer our first question: the special thing about
 semisimple algebras is that the relationship between their indecomposable
 modules and their simple modules is much clearer. Namely\dots
 
-\begin{proposition}\label{thm:complete-reducibility-equiv}
+\begin{proposition}
   Given a finite-dimensional Lie algebra \(\mathfrak{g}\) over \(K\),
   \(\mathfrak{g}\) is semisimple if, and only if every finite-dimensional
   \(\mathfrak{g}\)-module is completely reducible.