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: c37732113c53393e5b48794104a7547dccf0cfc0
Parent: 91c6c49f999e57ef3f96ebbc15e2696939346770
Author: Pablo <pablo-escobar@riseup.net>
Date: Thu, 20 Apr 2023 21:54:01 +0000

Minor improvement in notation

Diffstat

1 file changed, 3 insertions, 4 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	7	3	4

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -714,10 +714,9 @@ century. Specifically, we find\dots
   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
   operators in \(G\) -- i.e. the algebra of all differential operators \(P :
-  C^\infty(G) \to C^\infty(G)\) such that \((P(f \circ \ell_g)) \circ
-  \ell_{g^{-1}} = P f\) for all \(f \in C^\infty(G)\) and \(g \in G\). There is
-  a canonical isomorphism of algebras \(\mathcal{U}(\mathfrak{g}) \isoto
-  \operatorname{Diff}(G)^G\).
+  C^\infty(G) \to C^\infty(G)\) such that \(g \cdot P f = P (g \cdot f)\) for
+  all \(f \in C^\infty(G)\) and \(g \in G\). There is a canonical isomorphism
+  of algebras \(\mathcal{U}(\mathfrak{g}) \isoto \operatorname{Diff}(G)^G\).
 \end{proposition}
 
 \begin{proof}