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: 359ba13be83cec73625eb06292c59f449700e814
Parent: 325ddfd3b5ef5838391398b4b791f07f06d972dc
Author: Pablo <pablo-escobar@riseup.net>
Date: Sun, 27 Nov 2022 16:53:00 +0000
Cleaned the references
Removed unused references and added missing informations
Diffstat

1 file changed, 59 insertions, 169 deletions
Status	File Name	N° Changes	Insertions	Deletions
Modified	references.bib	228	59	169
diff --git a/references.bib b/references.bib
@@ -1,146 +1,44 @@
 @book{serganova,
   title =     {A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras},
-  author =    {Caroline Gruson, Vera Serganova},
+  author =    {Gruson, Caroline and Serganova, Vera},
   year =      {2018},
 }
 
-@book{alexandrino,
-  title =  {Notas de Aula de MAT5771},
-  author = {Marcos Alexandrino},
-  year =   {2019},
-  url =    {https://www.ime.usp.br/~malex/arquivos/lista2019/GeoRiemanniana-Main-novo2019.pdf},
-}
-
 @book{fulton-harris,
-  title =     {Representation theory: A first course},
-  author =    {William Fulton, Joe Harris},
+  title =     {Representation Theory: A First Course},
+  author =    {Fulton, William and Harris, Joe},
   publisher = {Springer},
   year =      {1991},
   series =    {Graduate Texts in Mathematics / Readings in Mathematics},
   edition =   {Corrected},
 }
 
-@book{san-martin-algebras,
-  title =     {Álgebras de Lie},
-  author =    {Luiz Antonio Barrera San Martin},
-  publisher = {Unicamp},
-  year =      {1999},
-  edition =   {1},
-}
-
-@book{san-martin-grupos,
-  title =     {Grupos de Lie},
-  author =    {Luiz A. B. San Martin},
-  publisher = {Unicamp},
-  year =      {2016},
-}
-
-@book{procesi,
-  title =     {Lie Groups: An Approach through Invariants and Representations},
-  author =    {Claudio Procesi},
-  publisher = {Springer},
-  year =      {2006},
-  series =    {Universitext},
-  edition =   {1},
-}
-
 @book{etingof,
   title =     {Introduction to Representation Theory},
-  author =    {Pavel Etingof},
+  author =    {Etingof, Pavel and Golberg, Oleg and Hensel, Sebastian and Liu, Tiankai and Schwendner, Alex  and Vaintrob, Dmitry and Yudovina, Elena},
   publisher = {American Mathematical Society},
   year =      {2011},
   series =    {Student Mathematical Library},
 }
 
-@book{fourier-on-number-fields,
-  title =     {Fourier Analysis on Number Fields},
-  author =    {Dinakar Ramakrishnan, Robert J. Valenza},
-  publisher = {Springer},
-  year =      {1998},
-  series =    {Graduate Texts in Mathematics v. 186},
-  edition =   {1},
-}
-
-@book{lie-theorems,
-  title  = {LECTURE 12: LIE'S FUNDAMENTAL THEOREMS},
-  author = {Zuoqin Wang},
-  year   = {2013},
-  url    = {http://staff.ustc.edu.cn/~wangzuoq/Courses/13F-Lie/Lie.html}
-}
-
-@book{gorodski,
-  title  = {Lecture Notes on Compact Lie Groups and Their Representation -- Prelimimary version},
-  author = {Claudio Gorodski},
-  year   = {2021},
-  url    = {https://www.ime.usp.br/~gorodski/teaching/mat6001/16.11.pdf}
-}
-
-@book{intro-to-lie-groups,
-  title =     {Introduction to Lie groups},
-  author =    {Joseph Hundley},
-  publisher = {Southern Illinois University Carbondale},
-  year =      {2009},
-  series =    {Miscellaneous (presentations, translations, interviews, etc)},
-  volume =    {Paper 42},
-  url =       {https://opensiuc.lib.siu.edu/math_misc/42/}
-}
-
-@book{fegan,
-  title =     {Introduction To Compact Lie Groups},
-  author =    {Howard D Fegan},
-  publisher = {World Scientific},
-  isbn =      {9810236867},
-  year =      {1991},
-  series =    {Series in Pure Mathematics},
-}
-
 @book{kirillov,
-  title =     {Introduction to Lie groups and Lie algebras},
-  author =    {Alexander Kirillov},
+  title =     {Introduction to Lie Groups and Lie Algebras},
+  author =    {Kirillov, Alexander},
   publisher = {Cambridge University Press},
   year =      {2008},
   url =       {https://www.math.stonybrook.edu/~kirillov/liegroups},
 }
 
 @book{lie-groups-serganova-student,
-  title =  {261A Lie Groups},
-  author = {Qiaochu Yuan},
-  year =   {2013},
-  url =    {https://math.berkeley.edu/~qchu/Notes/261A.pdf},
-}
-
-@misc{geometric-representation-williason,
-  title =     {Representation theory and geometry },
-  author =    {Geordie Williamson},
-  year =      {2018},
-  publisher = {2018 Internatition Congress of Mathematicians},
-  series =    {Plenary Lectures},
-  url =       {https://www.youtube.com/watch?v=-3q6C558yog},
-}
-
-@article{moore,
-  doi =        {10.2140/pjm.1962.12.359},
-  year =       {1962},
-  month =      mar,
-  publisher =  {Mathematical Sciences Publishers},
-  volume =     {12},
-  number =     {1},
-  pages =      {359--365},
-  author =     {Calvin Moore},
-  title =      {On the Frobenius reciprocity theorem for locally compact groups},
-  journal =    {Pacific Journal of Mathematics}
-}
-
-@book{cx-lie,
-  title  = {Notes on complex Lie groups},
-  author = {Dietmar A. Salamon},
-  year   = {2019},
-  url    = {https://people.math.ethz.ch/~salamon/PREPRINTS/cx-lie.pdf}
+  title =     {261A Lie Groups},
+  author =    {Yuan, Qiaochu},
+  year =      {2013},
+  url =       {https://math.berkeley.edu/~qchu/Notes/261A.pdf},
 }
 
 @book{humphreys,
-  title =     {Introduction to Lie algebras and representation theory},
-  author =    {J.E. Humphreys},
+  title =     {Introduction to Lie Algebras and Representation Theory},
+  author =    {E. Humphreys, James},
   publisher = {Springer},
   year =      {1973},
   series =    {Graduate Texts in Mathematics},
@@ -148,48 +46,40 @@
 }
 
 @inproceedings{cohomologies-lie,
-  booktitle =  {Lie Groups and Lie Algebras II},
-  title =      {Cohomologies of Lie Groups and Lie Algebras},
-  author =     {Boris L. Feigin, Dmitry B. Fuchs},
-  publisher =  {Springer},
-  series =     {Encyclopedia of Mathematics},
-  volume =     21,
-  year =       {2000},
-}
-
-@article{unitary-group-strong-topology,
-  doi =       {10.48550/ARXIV.1309.5891},
-  author =    {Schottenloher, Martin},
-  title =     {The Unitary Group In Its Strong Topology},
-  publisher = {arXiv},
-  year =      {2013},
+  booktitle = {Lie Groups and Lie Algebras II},
+  title =     {Cohomologies of Lie Groups and Lie Algebras},
+  author =    {L. Feigin, Boris and B. Fuchs, Dmitry},
+  publisher = {Springer},
+  series =    {Encyclopedia of Mathematics},
+  volume =    21,
+  year =      {2000},
 }
 
 @book{harder,
   title =     {Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces},
-  author =    {G{\"u}nter Harder},
+  author =    {Harder, G{\"u}nter},
   year =      {2008},
   publisher = {Springer}
 }
 
 @book{ribeiro,
-  title =  {Notes of Everything},
-  author = {Gabriel Ribeiro},
-  year =   {2022},
-  url =    {https://perso.pages.math.cnrs.fr/users/gabriel.ribeiro/assets/files/main.pdf}
+  title =     {Notes of Everything},
+  author =    {Ribeiro, Gabriel},
+  year =      {2022},
+  url =       {https://perso.pages.math.cnrs.fr/users/gabriel.ribeiro/assets/files/main.pdf}
 }
 
 @book{symplectic-physics,
-  title =     {Symplectic techniques in physics},
-  author =    {Victor Guillemin, Shlomo Sternberg},
+  title =     {Symplectic Techniques in Physics},
+  author =    {Guillemin, Victor and Sternberg, Shlomo},
   publisher = {Cambridge University Press},
   year =      {1984},
   edition =   {First Edition},
 }
 
 @book{goodearl-warfield,
-  title =     {An introduction to noncommutative noetherian rings},
-  author =    {Goodearl K.R., Warfield Jr R.B.},
+  title =     {An Introduction to Noncommutative Noetherian Rings},
+  author =    {R. Goodearl, Kenneth and Warfield Jr, Robert B.},
   publisher = {Cambridge University Press},
   year =      {2004},
   series =    {London Mathematical Society Student Texts},
@@ -198,7 +88,7 @@
 
 @misc{dimitar-exp,
   doi =       {10.48550/ARXIV.2011.09975},
-  author =    {Dimitar Grantcharov, Khoa Nguyen},
+  author =    {Grantcharov, Dimitar and Nguyen, Khoa},
   title =     {Exponentiation and Fourier transform of tensor modules of $\mathfrak { sl} (n+1)$},
   publisher = {arXiv},
   year =      {2020},
@@ -206,28 +96,30 @@
 }
 
 @article{nilsson,
-  title =   {$\mathcal{U}(\mathfrak{g})$-free modules and coherent families},
-  journal = {Journal of Pure and Applied Algebra},
-  volume =  {220},
-  number =  {4},
-  pages =   {1475-1488},
-  year =    {2016},
-  doi =     {https://doi.org/10.1016/j.jpaa.2015.09.013},
-  author =  {Jonathan Nilsson},
+  title =     {$\mathcal{U}(\mathfrak{g})$-free modules and coherent families},
+  journal =   {Journal of Pure and Applied Algebra},
+  author =    {Nilsson, Jonathan},
+  volume =    {220},
+  number =    {4},
+  pages =     {1475-1488},
+  year =      {2016},
+  doi =       {https://doi.org/10.1016/j.jpaa.2015.09.013},
 }
 
 @article{fernando,
-  title =   {Lie algebra modules with finite-dimensional weight spaces. I},
-  author =  {S Rupasiri Lakshman Fernando},
-  journal = {Transactions of the American Mathematical Society},
-  year =    {1990},
-  volume =  {322},
-  pages =   {757-781},
+  title =     {Lie algebra modules with finite-dimensional weight spaces. I},
+  author =    {Rupasiri Lakshman Fernando},
+  journal =   {Transactions of the American Mathematical Society},
+  doi =       {10.1090/S0002-9947-1990-1013330-8},
+  year =      {1990},
+  volume =    {322},
+  pages =     {757-781},
 }
 
 @article{mathieu,
   author =    {Mathieu, Olivier},
   journal =   {Annales de l'institut Fourier},
+  doi =       {10.5802/aif.1765},
   number =    {2},
   pages =     {537-592},
   publisher = {Association des Annales de l'Institut Fourier},
@@ -237,26 +129,24 @@
 }
 
 @book{demazure-gabriel,
-   title =     {Groupes Algebriques Tome 1},
-   author =    {Demazure M., Gabriel P.},
-   publisher = {NH},
-   isbn =      {9780720420340},
-   year =      {1970},
+  title =     {Groupes Algebriques Tome 1},
+  author =    {Demazure, Michel and Gabriel, Pierre},
+  publisher = {NH},
+  year =      {1970},
 }
 
 @book{coutinho,
-   title =     {A primer of algebraic D-modules},
-   author =    {S. C. Coutinho},
-   publisher = {Cambridge University Press},
-   isbn =      {0521551196},
-   year =      {1995},
-   series =    {London Mathematical Society student texts 33},
+  title =     {A Primer of Algebraic $D$-modules},
+  author =    {C. Coutinho, Severino},
+  publisher = {Cambridge University Press},
+  year =      {1995},
+  series =    {London Mathematical Society student texts 33},
 }
 
 @article{frobenius,
-  title={{\"U}ber Gruppencharakteren},
-  author={Frobenius, F Georg},
-  journal={Wiss. Berlin},
-  pages={985--1021},
-  year={1896}
+  title =     {{\"U}ber Gruppencharakteren},
+  author =    {Frobenius, Ferdiand Georg},
+  journal =   {Wiss. Berlin},
+  pages =     {985--1021},
+  year =      {1896}
 }