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: 5b7bf9c8ee990e2e5ecf05036eee58724b1cb2a5
Parent: 65e93388cd80c096674dbfa5510dedb2ce0c8165
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 23 Apr 2023 00:59:49 +0000

Fixed a minor typo

Diffstat

1 file changed, 3 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	6	3	3

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -608,9 +608,9 @@ This is all well and good, but what does any of this have to do with complete
 reducibility? Well, in general cohomology theories really shine when one is
 trying to control obstructions of some kind. In our case, the bifunctor
 \(H^1(\mathfrak{g}, \operatorname{Hom}(-, -)) :
-\mathfrak{g}\text{-}\mathbf{Mod} \times \mathfrak{g}\text{-}\mathbf{Mod} \to
-\mathbf{Ab}\) classifies obstructions to complete reducibility.
-Explicitly\dots
+\mathfrak{g}\text{-}\mathbf{Mod}^{\operatorname{op}} \times
+\mathfrak{g}\text{-}\mathbf{Mod} \to K\text{-}\mathbf{Vect}\) classifies
+obstructions to complete reducibility. Explicitly\dots
 
 \begin{theorem}
   Given \(\mathfrak{g}\)-modules \(N\) and \(L\), there is a one-to-one