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: ac770d9ef731fe6ff71d7edb2d4e7175faeddcfe
Parent: 4309462aa340a65210b2cd27fb7733668e220d47
Author: Pablo <pablo-escobar@riseup.net>
Date: Fri, 11 Nov 2022 23:07:27 +0000
Formatted references.bib
Diffstat

1 file changed, 126 insertions, 140 deletions
Status	File Name	N° Changes	Insertions	Deletions
Modified	references.bib	266	126	140
diff --git a/references.bib b/references.bib
@@ -1,76 +1,64 @@
 @book{serganova,
- title =     {A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras},
- author =    {Caroline Gruson, Vera Serganova},
- publisher = {},
- year =      {2018},
- series =    {},
- edition =   {},
- volume =    {},
+  title =     {A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras},
+  author =    {Caroline Gruson, Vera Serganova},
+  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},
+  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},
-   publisher = {Springer},
-   year =      {1991},
-   series =    {Graduate Texts in Mathematics / Readings in Mathematics},
-   edition =   {Corrected},
-   volume =    {},
+  title =     {Representation theory: A first course},
+  author =    {William Fulton, Joe Harris},
+  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},
-   series =    {},
-   edition =   {1},
-   volume =    {},
+  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},
-   series =    {},
-   edition =   {},
-   volume =    {},
+  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},
-   volume =    {},
+  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},
-   publisher = {American Mathematical Society},
-   year =      {2011},
-   series =    {Student Mathematical Library},
+  title =     {Introduction to Representation Theory},
+  author =    {Pavel Etingof},
+  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},
-   volume =    {},
+  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,
@@ -86,63 +74,61 @@
   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)},
- edition =   {},
- volume =    {Paper 42},
- url =       {https://opensiuc.lib.siu.edu/math_misc/42/}
+  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},
+  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},
- publisher = {Cambridge University Press},
- year =      {2008},
- series =    {},
- url =       {https://www.math.stonybrook.edu/~kirillov/liegroups},
+  title =     {Introduction to Lie groups and Lie algebras},
+  author =    {Alexander Kirillov},
+  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},
- series = {},
- url =    {https://math.berkeley.edu/~qchu/Notes/261A.pdf},
+  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},
+  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}
+  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,
@@ -153,79 +139,79 @@
 }
 
 @book{humphreys,
-   title =     {Introduction to Lie algebras and representation theory},
-   author =    {J.E. Humphreys},
-   publisher = {Springer},
-   year =      {1973},
-   series =    {Graduate Texts in Mathematics},
-   edition =   {1},
+  title =     {Introduction to Lie algebras and representation theory},
+  author =    {J.E. Humphreys},
+  publisher = {Springer},
+  year =      {1973},
+  series =    {Graduate Texts in Mathematics},
+  edition =   {1},
 }
 
 @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},
+  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},
+  doi =       {10.48550/ARXIV.1309.5891},
+  author =    {Schottenloher, Martin},
+  title =     {The Unitary Group In Its Strong Topology},
   publisher = {arXiv},
-  year = {2013},
+  year =      {2013},
 }
 
 @book{harder,
-  title={Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces},
-  author={G{\"u}nter Harder},
-  year={2008},
-  publisher={Springer}
+  title =     {Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces},
+  author =    {G{\"u}nter Harder},
+  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 = {Gabriel Ribeiro},
+  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},
-   publisher = {Cambridge University Press},
-   year =      {1984},
-   edition =   {First Edition},
+  title =     {Symplectic techniques in physics},
+  author =    {Victor Guillemin, Shlomo Sternberg},
+  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.},
-   publisher = {Cambridge University Press},
-   year =      {2004},
-   series =    {London Mathematical Society Student Texts},
-   edition =   {Second Edition},
+  title =     {An introduction to noncommutative noetherian rings},
+  author =    {Goodearl K.R., Warfield Jr R.B.},
+  publisher = {Cambridge University Press},
+  year =      {2004},
+  series =    {London Mathematical Society Student Texts},
+  edition =   {Second Edition},
 }
 
 @misc{dimitar-exp,
-  doi = {10.48550/ARXIV.2011.09975},
-  author = {Dimitar Grantcharov, Khoa Nguyen},
-  title = {Exponentiation and Fourier transform of tensor modules of $\mathfrak{sl} (n+1)$},
+  doi =       {10.48550/ARXIV.2011.09975},
+  author =    {Dimitar Grantcharov, Khoa Nguyen},
+  title =     {Exponentiation and Fourier transform of tensor modules of $\mathfrak { sl} (n+1)$},
   publisher = {arXiv},
-  year = {2020},
+  year =      {2020},
   copyright = {Creative Commons Zero v1.0 Universal}
 }
 
 @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},
+  volume =  {220},
+  number =  {4},
+  pages =   {1475-1488},
+  year =    {2016},
+  doi =     {https://doi.org/10.1016/j.jpaa.2015.09.013},
+  author =  {Jonathan Nilsson},
 }