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: 59f4eea9478b9d6311052b0411f04b50cbca6212
Parent: b10f1352dfb0b9b52767bed1944bcb716c87d810
Author: Pablo <pablo-escobar@riseup.net>
Date: Tue, 20 Dec 2022 10:34:48 +0000

Added a reference to the concept of adjoint functors

Diffstat

2 files changed, 10 insertions, 1 deletion

Status	File Name	N° Changes	Insertions	Deletions
Modified	references.bib	8	8	0
Modified	sections/introduction.tex	3	2	1

diff --git a/references.bib b/references.bib
@@ -150,3 +150,11 @@
   pages =     {985--1021},
   year =      {1896}
 }
+
+@book{maclane,
+   title =     {Categories for the working mathematician},
+   author =    {Mac Lane, Saunders},
+   publisher = {Springer-Verlag},
+   year =      {1971},
+   edition =   {6},
+}

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -638,7 +638,8 @@ It is important to note, however, that \(\mathcal{U} : K\text{-}\mathbf{LieAlg}
 \(\mathfrak{g} = K\) is the \(1\)-dimensional Abelian Lie algebra then
 \(\mathcal{U}(\mathfrak{g}) \cong K[x]\), which is infinite-dimensional.
 Nevertheless, Proposition~\ref{thm:universal-env-uni-prop} may be restated
-as\dots
+using the language of adjoint functors -- as described in \cite{maclane} for
+instance.
 
 \begin{corollary}
   If \(\operatorname{Lie} : K\text{-}\mathbf{Alg} \to