- Commit
- 2bfc38f7eb48922dc9b04a603edd0d4aaed9c155
- Parent
- 262948b5117fff49dff676be7289b3693cc87207
- Author
- Pablo <pablo-escobar@riseup.net>
- Date
Added proper references to the chapter on Mathieu's work to the chapter on semisimple Lie algebras
Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules
Added proper references to the chapter on Mathieu's work to the chapter on semisimple Lie algebras
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