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: 391dfe0dd595bd515e2ec712213ac2106300bd98
Parent: 0bd82ae0c129ec102c4bc6897bd70b5221169b81
Author: Pablo <pablo-escobar@riseup.net>
Date: Thu, 13 Oct 2022 23:20:21 +0000

Fixed a minor error

Diffstat

1 file changed, 3 insertions, 4 deletions

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

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -488,11 +488,10 @@
 
 \begin{definition}
   Let \(R\) be a ring. A subset \(S \subset R\) is called \emph{multiplicative}
-  if \(s \cdot t \in S\) for all \(s, t \in S\) and \(0 \notin S\).
-  A multiplicative subset \(S\) is said to satisfy \emph{Ore's localization
+  if \(s \cdot t \in S\) for all \(s, t \in S\) and \(0 \notin S\). A
+  multiplicative subset \(S\) is said to satisfy \emph{Ore's localization
   condition} if for each \(r \in R\), \(s \in S\) there exists \(u_1, u_2 \in
-  R\) and \(t_1, t_2 \in S\) such that \(s^{-1} r = u_1 t_1^{-1}\) and \(r
-  s^{-1} = t_2^{-1} u_2\).
+  R\) and \(t_1, t_2 \in S\) such that \(s r = u_1 t_1\) and \(r s = t_2 u_2\).
 \end{definition}
 
 \begin{theorem}[Ore-Asano]