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: 30591dc47f8faefd7cb7b0903b0b6e056bf50942
Parent: dba0653482d86747f1446e39262fb9b0506aba4c
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 16 Nov 2022 15:49:34 +0000

Fixed a typo

Diffstat

1 file changed, 3 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	5	3	2

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -442,8 +442,8 @@
   \mathfrak{g}}{I}\).
   \begin{center}
     \begin{tikzcd}
-      T \mathfrak{g} \arrow{dr}{\bar{g}}           & \\
-      \mathcal{U}(\mathfrak{g}) \uar \rar[swap]{g} & A
+      T \mathfrak{g} \rar{g} \dar                         & A \\
+      \mathcal{U}(\mathfrak{g}) \arrow[swap]{ur}{\bar{g}} &
     \end{tikzcd}
   \end{center}
 
@@ -530,6 +530,7 @@
   \operatorname{Ind}_{\mathfrak{h}}^{\mathfrak{g}}\).
 \end{proposition}
 
+% TODO: Define the algebra of differential operators of a given algebra
 \begin{proposition}
   Let \(G\) be a Lie group and \(\mathfrak{g}\) be its Lie algebra. Denote by
   \(\operatorname{Diff}(G)^G\) the algebra of \(G\)-invariant differential