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: 6b122954d025571e7a4ca57d1123ffbebdb13727
Parent: 3a4bb936967714ddfb3a42e1648dbec8e343a4bc
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 21 Dec 2022 17:31:38 +0000

Added a clarification

Added further details on Weyl's proof of complete reducibility

Diffstat

1 file changed, 2 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	4	2	2

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -358,8 +358,8 @@ complexification of the Lie algebra of a unique simply connected compact Lie
 group, known as its \emph{compact form}. Hence the category of the
 finite-dimensional representations of a given complex semisimple algebra is
 equivalent to that of the finite-dimensional smooth representations of its
-compact form, whose representations are known to be completely reducible -- see
-\cite[ch. 3]{serganova} for instance.
+compact form, whose representations are known to be completely reducible
+because of Maschke's Theorem -- see \cite[ch. 3]{serganova} for instance.
 
 This proof, however, is heavily reliant on the geometric structure of
 \(\mathbb{C}\). In other words, there is no hope for generalizing this for some