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: 6b00f2793868e825ba9ff67b4dac22c20f3ea6ea
Parent: d0aecccb60a0dc077bb08b750edba81cab02c2b9
Author: Pablo <pablo-escobar@riseup.net>
Date: Sat, 17 Dec 2022 21:57:31 +0000

Added the definition of the dimension of a Lie algebra

Diffstat

1 file changed, 2 insertions, 1 deletion

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	3	2	1

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -35,7 +35,8 @@ called \emph{Lie algebras}, and these will be the focus of these notes.
   \[
     f([X, Y]) = [f(X), f(Y)]
   \]
-  for all \(X, Y \in \mathfrak{g}\).
+  for all \(X, Y \in \mathfrak{g}\). The dimension \(\dim \mathfrak{g}\) of
+  \(\mathfrak{g}\) is its dimension as a \(K\)-vector space.
 \end{definition}
 
 The collection of Lie algebras over a fixed field \(K\) thus form a category,