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: d4aff46c38d5b8e35d7753d241db15611a9e3d81
Parent: 4cc54e0bc8d0018b0446e2dccb22b9189aff113a
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 25 Nov 2022 15:49:10 +0000

Clarified some notation

Diffstat

1 file changed, 6 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	9	6	3

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -844,7 +844,9 @@ representations.
     \end{tikzcd}
   \end{center}
   commutes for all \(X \in \mathfrak{g}\). We denote the space of all
-  intertwiners \(V \to W\) by \(\operatorname{Hom}_{\mathfrak{g}}(V, W)\).
+  intertwiners \(V \to W\) by \(\operatorname{Hom}_{\mathfrak{g}}(V, W)\) -- as
+  opposed the the space \(\operatorname{Hom}(V, W)\) of all \(K\)-linear maps
+  \(V \to W\).
 \end{definition}
 
 The collection of representations of a fixed Lie algebra \(\mathfrak{g}\) thus
@@ -923,8 +925,9 @@ define\dots
 
 \begin{example}
   Given a Lie algebra \(\mathfrak{g}\) and representations \(V\) and \(W\) of
-  \(\mathfrak{g}\), the spaces \(V \wedge W\) and \(V \odot W\) are both
-  representations of \(\mathfrak{g}\): they are quotients of \(V \otimes W\).
+  \(\mathfrak{g}\), the exterior and symmetric products \(V \wedge W\) and \(V
+  \odot W\) are both representations of \(\mathfrak{g}\): they are quotients of
+  \(V \otimes W\).
 \end{example}
 
 \begin{example}