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: f309228f6d154eb47775ecb965743540bcb1f23b
Parent: f8134e9f4ceb60d6a4b92b854d7e04d7beeda1e6
Author: Pablo <pablo-escobar@riseup.net>
Date: Tue, 25 Apr 2023 23:52:32 +0000

Clarified a sentence

Diffstat

1 file changed, 4 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	6	4	2

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -628,8 +628,10 @@ obstructions to complete reducibility. Explicitly\dots
 This is essentially a consequence of Example~\ref{ex:hom-invariants-are-g-homs}
 and Theorem~\ref{thm:ext-1-classify-short-seqs}, as well as the minimality
 conditions that characterize \(\operatorname{Ext}^1\). For the readers already
-familiar with homological algebra: this natural isomorphism can be explicitly
-described by considering a canonical free resolution
+familiar with homological algebra: the correspondence between
+\(H^1(\mathfrak{g}, \operatorname{Hom}(L, N))\) and short exact sequences of
+\(\mathfrak{g}\)-modules can be described in very concrete terms by considering
+a canonical free resolution
 \begin{center}
   \begin{tikzcd}
     \cdots                                                    \rar[dashed] &