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: 32a36d3fc2f33d67a66cfca96347b0f5f753edcf
Parent: 394316a2ae25e18e2837eed4a8d0ce137c811fa6
Author: Pablo <pablo-escobar@riseup.net>
Date: Mon, 21 Nov 2022 00:12:01 +0000

Reordered some equations

Diffstat

1 file changed, 3 insertions, 3 deletions

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

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -744,11 +744,11 @@ terms of an action of \(\mathfrak{g}\) in a vector space and write simply \(X
   The space \(K[x, y]\) is a representation of \(\mathfrak{sl}_2(K)\) with
   \begin{align*}
     e \cdot p & = x \frac{\mathrm{d}}{\mathrm{d}y} p &
+    f \cdot p & = y \frac{\mathrm{d}}{\mathrm{d}x} p &
     h \cdot p & =
     \left(
-    x \frac{\mathrm{d}}{\mathrm{d}x} - y \frac{\mathrm{d}}{\mathrm{d}y}
-    \right) p &
-    f \cdot p & = y \frac{\mathrm{d}}{\mathrm{d}x} p &
+      x \frac{\mathrm{d}}{\mathrm{d}x} - y \frac{\mathrm{d}}{\mathrm{d}y}
+    \right) p
   \end{align*}
 \end{example}