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: 238d43d057209dd9e5a584d35286cf3284c19402
Parent: 4f800549d96246c5cdde1b5fcc18b8437dfc6374
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 27 Nov 2022 15:19:23 +0000

Fixed a typo

Diffstat

1 file changed, 1 insertion, 1 deletion

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/complete-reducibility.tex	2	1	1

diff --git a/sections/complete-reducibility.tex b/sections/complete-reducibility.tex
@@ -86,7 +86,7 @@ this is not always the case. For instance\dots
   is a representation of the Lie algebra \(K[x]\). Notice \(V\) has a single
   nonzero proper subrepresentation, which is spanned by the vector \((1, 0)\).
   This is because if \((a + b, b) = \rho(x) \ (a, b) = \lambda (a, b)\) for
-  some \(\lambda \in \mathbb{C}\) then \(\lambda = 1\) and \(b = 0\). Hence \(V\) is
+  some \(\lambda \in K\) then \(\lambda = 1\) and \(b = 0\). Hence \(V\) is
   indecomposable -- it cannot be broken into a direct sum of 1-dimensional
   subrepresentations -- but it is evidently not irreducible.
 \end{example}