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: 2bfc38f7eb48922dc9b04a603edd0d4aaed9c155
Parent: 262948b5117fff49dff676be7289b3693cc87207
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 25 Sep 2022 14:43:06 +0000

Added proper references to the chapter on Mathieu's work to the chapter on semisimple Lie algebras

Diffstat

2 files changed, 3 insertions, 3 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/mathieu.tex	2	1	1
Modified	sections/semisimple-algebras.tex	4	2	2

diff --git a/sections/mathieu.tex b/sections/mathieu.tex
@@ -1,4 +1,4 @@
-\chapter{Irreducible Weight Modules}
+\chapter{Irreducible Weight Modules}\label{ch:mathieu}
 
 \begin{definition}
   A representation \(V\) of \(\mathfrak{g}\) is called a \emph{weight

diff --git a/sections/semisimple-algebras.tex b/sections/semisimple-algebras.tex
@@ -12,7 +12,6 @@ Lie algebra? This is a question that have sparked an entire field of research,
 and we cannot hope to provide a comprehensive answer the 40 pages we have left.
 Nevertheless, we can work on particular cases.
 
-% TODO: Add a reference to the next chapter when it's done
 Like any sane mathematician would do, we begin by studying a simpler case. The
 restrictions we impose are twofold: restrictions on the algebras whose
 representations we'll classify, and restrictions on the representations
@@ -21,7 +20,8 @@ algebras over an algebraically closed field \(K\) of characteristic \(0\). This
 is a restriction we will carry throughout these notes. Moreover, as indicated
 by the title of this chapter, we will initially focus on the so called
 \emph{semisimple} Lie algebras algebras -- we will later relax this restriction
-a bit in the next chapter when we dive into \emph{reductive} Lie algebras.
+a bit in chapter~\ref{ch:mathieu} when we dive into \emph{reductive} Lie
+algebras.
 
 There are multiple equivalent ways to define what a semisimple Lie algebra is.
 Perhaps the most common definition is\dots