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: 647da297f343c127fdb5ce1513c30c3a6c8dc51c
Parent: 41970a21d4049b597fabe37789921cc30cbfe48b
Author: Pablo <pablo-escobar@riseup.net>
Date: Tue, 25 Apr 2023 00:46:13 +0000

Fixed the name of the standard resolution of the trivial module

Diffstat

1 file changed, 4 insertions, 4 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	8	4	4

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -639,10 +639,10 @@ concretely by considering a canonical free resolution
     0
   \end{tikzcd}
 \end{center}
-of the trivial \(\mathfrak{g}\)-module \(K\), known as \emph{the standard
-resolution}, which provides an explicit construction of the cohomology groups
--- see \cite[sec.~1.3C]{cohomologies-lie} or \cite[sec.~24]{symplectic-physics}
-for further details.
+of the trivial \(\mathfrak{g}\)-module \(K\), known as \emph{the
+Chevalley-Eilenberg resolution}, which provides an explicit construction of the
+cohomology groups -- see \cite[sec.~1.3C]{cohomologies-lie} or
+\cite[sec.~24]{symplectic-physics} for further details.
 
 We will use the previous result implicitly in our proof, but we will not prove
 it in its full force. Namely, we will show that if \(\mathfrak{g}\) is