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: d16a340f6b4df5c2bbc75d4da4fb27372adcca2d
Parent: 7e9e9bc4fa3f8a3a3c898334bc0c38a5c5f18762
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 9 Apr 2023 22:44:17 +0000

Minor tweak in notation

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
@@ -336,7 +336,7 @@ characterization of finite-dimensional semisimple Lie algebras, known as
         \kappa_M : \mathfrak{g} \times \mathfrak{g}                          &
         \to K                                                                \\
         (X, Y)                                                               &
-        \mapsto \operatorname{Tr}(X\!\restriction_M \circ Y\!\restriction_M)
+        \mapsto \operatorname{Tr}(X\!\restriction_M \, Y\!\restriction_M)
       \end{align*}
       is non-degenerate\footnote{A symmetric bilinear form $B : \mathfrak{g}
       \times \mathfrak{g} \to K$ is called non-degenerate if $B(X, Y) = 0$ for