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: d0cbf9ca62547857bfa820c7ae70ad7f4de098ff
Parent: 0904c078698220fd2d642ed7e993eb7d3b7c7be1
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 2 Jan 2023 01:26:50 +0000

Fixed a typo

The Ext functors are contravariant in the first entry

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
@@ -385,9 +385,9 @@ basic}. In fact, all we need to know is\dots
 
 \begin{theorem}\label{thm:ext-exacts-seqs}\index{\(\operatorname{Ext}\) functors}
   There is a sequence of bifunctors \(\operatorname{Ext}^i :
-  \mathfrak{g}\text{-}\mathbf{Mod} \times \mathfrak{g}\text{-}\mathbf{Mod} \to
-  K\text{-}\mathbf{Vect}\), \(i \ge 0\) such that, given a
-  \(\mathfrak{g}\)-module \(L'\), every exact sequence of
+  \mathfrak{g}\text{-}\mathbf{Mod}^{\operatorname{op}} \times
+  \mathfrak{g}\text{-}\mathbf{Mod} \to K\text{-}\mathbf{Vect}\), \(i \ge 0\)
+  such that, given a \(\mathfrak{g}\)-module \(L'\), every exact sequence of
   \(\mathfrak{g}\)-modules
   \begin{center}
     \begin{tikzcd}