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
Log
Files
Refs
README
LICENSE

Commit: 1fe64a4d40f205543a6ea36e046888d81f4b103f
Parent: 6a73599f82d2b135bd19785fb160180205291070
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 11 Sep 2022 01:12:18 +0000

Clarified a corolarry on Lie algebra cohomology

Diffstat

1 file changed, 10 insertions, 2 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/semisimple-algebras.tex	12	10	2

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -314,9 +314,17 @@ implies\dots
                           |- (X.center) \tikztonodes
                           -| ([xshift=-2ex]\tikztotarget.west)
                           -- (\tikztotarget)}]{dll}[at end]{} \\ &
-      H^1(\mathfrak{g}, W) \arrow[r] &
+      H^1(\mathfrak{g}, W) \arrow[r]\ar[draw=none]{d}[name=Y, anchor=center]{} &
       H^1(\mathfrak{g}, V) \arrow[r] &
-      H^1(\mathfrak{g}, U) \arrow[r, dashed] &
+      H^1(\mathfrak{g}, U)
+      \ar[rounded corners,
+                to path={ -- ([xshift=2ex]\tikztostart.east)
+                          |- (Y.center) \tikztonodes
+                          -| ([xshift=-2ex]\tikztotarget.west)
+                          -- (\tikztotarget)}]{dll}[at end]{} \\ &
+      H^2(\mathfrak{g}, W) \arrow[r] &
+      H^2(\mathfrak{g}, V) \arrow[r] &
+      H^2(\mathfrak{g}, U) \arrow[r, dashed] &
       \cdots
     \end{tikzcd}
   \end{center}