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

Commit
59f4eea9478b9d6311052b0411f04b50cbca6212
Parent
b10f1352dfb0b9b52767bed1944bcb716c87d810
Author
Pablo <pablo-escobar@riseup.net>
Date

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