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: e968ddebe30639e07a5622421a8c25ed7471a553
Parent: 3f990683edbc5c96f90041f768bf785bd7caf219
Author: Pablo <pablo-escobar@riseup.net>
Date: Tue, 20 Dec 2022 10:06:40 +0000

Added a reference to the non-fullyness of the Lie functor for algebraic groups

Diffstat

1 file changed, 1 insertion, 1 deletion

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	2	1	1

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -251,7 +251,7 @@ delicate in the algebraic case. For instance, given simply connected algebraic
 \(K\)-groups \(G\) and \(H\) with Lie algebras \(\mathfrak{g}\) and
 \(\mathfrak{h}\), respectively, there may be a homomorphism of Lie algebras
 \(\mathfrak{g} \to \mathfrak{h}\) which \emph{does not} come from a rational
-homomorphism \(G \to H\).
+homomorphism \(G \to H\) -- see \cite[ch.~II]{demazure-gabriel} for instance.
 
 In other words, the Lie functor \(K\text{-}\mathbf{Grp}_{\operatorname{simpl}}
 \to K\text{-}\mathbf{LieAlg}\) fails to be full. Furthermore, there are