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: 06cc1a53ecf4084e1b0322d45661715cb1c54849
Parent: 296df4283332a903db93f3a0a52e80849bf3765b
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 11 Nov 2022 23:50:14 +0000

Clarified a definition

Diffstat

1 file changed, 3 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	6	3	3

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -132,9 +132,9 @@ A particularly well behaved class of examples are the so called
 
 \begin{definition}
   A weight \(\mathfrak{g}\)-module is called \emph{admissible} if \(\dim
-  V_\lambda\) is bounded. The lowest upper bound for \(\dim V_\lambda\) is
-  called \emph{the degree of \(V\)}. The \emph{essential support} of \(V\) is
-  the set \(\operatorname{supp}_{\operatorname{ess}} V = \{ \lambda \in
+  V_\lambda\) is bounded. The lowest upper bound \(d\) for \(\dim V_\lambda\)
+  is called \emph{the degree of \(V\)}. The \emph{essential support} of \(V\)
+  is the set \(\operatorname{supp}_{\operatorname{ess}} V = \{ \lambda \in
   \mathfrak{h}^* : \dim V_\lambda = d \}\).
 \end{definition}