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: f6e4bb679dc8ee9d56e58798289e6409486ba4fe
Parent: 1dbcc654c5fc0b8868792f0f00e56f5db5ec8ec4
Author: Pablo <pablo-escobar@riseup.net>
Date: Wed, 21 Sep 2022 16:02:31 +0000

Added some items to the TODO list

Diffstat

1 file changed, 4 insertions, 0 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	TODO.md	4	4	0

diff --git a/TODO.md b/TODO.md
@@ -1,5 +1,9 @@
 # TODO
 
+* Prove that every finite-dimensional representation of a semisimple algebra is
+  a weight module
+* Prove that the action of the Casimir element is non-zero on non-trivial
+  irreducible modules
 * Write something on the motivation for the representation theory of Lie
   algebras
   * Main motivation: smooth representations of Lie groups and rational