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: f8134e9f4ceb60d6a4b92b854d7e04d7beeda1e6
Parent: 9369503bb587ce37286820382367fd7a076227b1
Author: Pablo <pablo-escobar@riseup.net>
Date: Tue, 25 Apr 2023 14:46:48 +0000

Added a clarification to the discussion on cohomology

Clarified the hypothesis of Levi's theorem

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
@@ -951,8 +951,8 @@ sequence
   \end{tikzcd}
 \end{center}
 
-This sequence always splits, which in light of
-Example~\ref{ex:all-simple-reps-are-tensor-prod} implies we can deduce
+This sequence always splits for finite-dimensional \(\mathfrak{g}\), which in
+light of Example~\ref{ex:all-simple-reps-are-tensor-prod} implies we can deduce
 information about \(\mathfrak{g}\)-modules by studying the modules of its
 ``semisimple part'' \(\mfrac{\mathfrak{g}}{\mathfrak{rad}(\mathfrak{g})}\) --
 see Proposition~\ref{thm:quotients-by-rads}. In practice this translates