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: 4cc54e0bc8d0018b0446e2dccb22b9189aff113a
Parent: 0cde29f05c4abbc5f69b5c318d86c1a6d8ae56a9
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 25 Nov 2022 15:45:34 +0000

Rewrote the preface

Diffstat

3 files changed, 39 insertions, 17 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	sections/introduction.tex	3	3	0
Modified	sections/preface.tex	50	36	14
Modified	tcc.tex	3	0	3

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -1,5 +1,8 @@
 \chapter{Introduction}
 
+\pagenumbering{arabic}
+\setcounter{page}{1}
+
 Associative algebras have proven themselves remarkably useful throughout
 mathematics. There's no lack of natural and interesting examples coming from a
 diverse spectrum of different fields: topology, number theory, analysis, you

diff --git a/sections/preface.tex b/sections/preface.tex
@@ -1,19 +1,41 @@
-\chapter*{About This Text}
+\chapter*{About These Notes}
 
-Throughout this notes we'll follow the following guiding principles:
+This is my undergraduate dissertation, produced in 2022 under the supervision
+of professor Iryna Kashuba of the department of mathematics of the Institute of
+Mathematics and Statistics of the Univety of São Paulo (IME-USP), Brazil.
 
-\begin{enumerate}
-  \item Lengthy proves are favored as opposed to collections of smaller lemmas.
-    This is a deliberate effort to emphasize the relevant results.
+Throughout this notes we'll follow some guiding principles. First, lengthy
+proves are favored as opposed to collections of smaller lemmas. This is a
+deliberate effort to emphasize the relevant results. Secondly, and this is more
+important, we are primarily interested in the broad strokes of the theory
+highlighted in the following chapters. The topic of the dissertation at hand,
+the resentation theory of Lie algebras, is a profoundly technical. In
+particular, certain proofs can sometimes feel like an unmotivated pile of
+technical arguments. Instead, we prefer to focus on the intuition behind the
+relevant results.
 
-  \item We prefer, whenever possible, to outsource proofs. This is because I
-    don't fancy reinventing the wheel: I'll write down proofs in here
-    \emph{only} when I fell like I have something to add to the proofs provided
-    by other materials. Otherwise we refer the reader to the proofs in other
-    books or articles -- which will likely be indicated just after the
-    statement of the theorem.
-\end{enumerate}
+Hence some results are left unproved. Nevertheless, we include numerous
+references throughout the text to other materials where the reader can find
+complete proofs. We'll assume basic knowledge of abstract algebra. In
+particular, we assume that the reader is familiarized with multilinear algebra
+and the theory of modules over a ring. Understanding some examples in the
+introductory chapter requires basic knowlage of differential and algebraic
+geometry, as well as rings of differential operators, but this examples are not
+necessary to the comprehension of the following chapters. Additional topics
+will be covered in the notes as needed.
 
-We'll assume basic knowledge of abstract algebra and module theory. Additional
-topics will be covered when needed.
+This document was typeset and compiled using free software. Its \LaTeX~source
+code is freely available at
+\url{https://git.pablopie.xyz/lie-algebras-and-their-representations/README.html},
+for distribution under the terms of the Creative Commons Attribution 4.0
+license.
 
+I would like to thank my parents for their love and support. I would specially
+like to thank professor Kashuba and Eduardo Monteiro Mendonça for their
+support. Their guidence over the past two years has profoundly shaped my
+passion for mathematics, and I could not have gotten to where I am now without
+their help. I suppose I should also thank them for enduring my chaotic
+digressions on the relationship between representation theory and geometry.
+Finally, I would like to thank my dear friend Lucas Dias Leme Schiezari for
+somehow convincing me to apply for a bachalors degree in pure mathematics. May
+he rest in peace.

diff --git a/tcc.tex b/tcc.tex
@@ -19,9 +19,6 @@
 
 \tableofcontents
 
-\pagenumbering{arabic}
-\setcounter{page}{1}
-
 \input{sections/introduction}
 
 \input{sections/complete-reducibility}