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: 95cb9df40af61351c4f7f8587a44e46fffca4dca
Parent: 30591dc47f8faefd7cb7b0903b0b6e056bf50942
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 16 Nov 2022 15:52:29 +0000

Fixed a typo

Diffstat

1 file changed, 4 insertions, 4 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	8	4	4

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -552,10 +552,10 @@
   \operatorname{Diff}(G)^G\) -- here \(\operatorname{Der}(G)^G \subset
   \operatorname{Der}(G)\) denotes the Lie subalgebra of invariant derivations.
 
-  Since \(f\) is a homomorphism of Lie algebras, it extends to an algebra
-  homomorphism \(g : \mathcal{U}(\mathfrak{g}) \to \operatorname{Diff}(G)^G\).
-  We claim \(g\) is an isomorphim. To see that \(g\) is injective, it suffices
-  to notice
+  Since \(f\) is a homomorphism of Lie algebras, it can be extended to an
+  algebra homomorphism \(g : \mathcal{U}(\mathfrak{g}) \to
+  \operatorname{Diff}(G)^G\). We claim \(g\) is an isomorphim. To see that
+  \(g\) is injective, it suffices to notice
   \[
     g(X_1 \cdots X_n)
     = g(X_1) \cdots g(X_n)