MS-E1200 - Lie groups and Lie algebras, 29.10.2019-18.12.2019

Materials

• Materials
  

  Materials

  A set of lecture notes is being written, which correspond quite accurately to the topics covered in the course. These notes are not in a polished form, and they are somewhat incomplete, and you should expect them to be updated with corrections, additions, and modifications regularly.

  • lecture notes
    

  
  

  
  

  Main textbook(s):

  We will mostly follow parts of the textbook

  • Fulton, W. & Harris, J.: Representation theory: a first course. 2004. 
    

  It has a strong emphasis on developing the theory by using examples.
  

  Another book which could be used as the textbook for this course is

  • Simon, B.: Representations of finite and compact groups. 1996.

  This one has an analysis flavor.
  
  

  
  

  Books on related topics, basic and advanced. 

  • Hall, Brian C., Lie Groups, Lie Algebras, and Representations, An Elementary Introduction. 2015

  • Armstrong, Mark, Groups and Symmetry, 1988  

  • Steinberg, B., Representation Theory of Finite Groups - An Introductory Approach. 2012

  • Berndt, Rolf, Representations of Linear Groups - An Introduction Based on Examples from Physics and Number Theory. 2007

  • Georgi, H., Lie Algebras In Particle Physics: from Isospin To Unified Theories. 1999 (a classic). 

  • Fuchs, J. and  Schweigert, C., Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists. 2003 (The first chapter is attached below which is an overview of different appearances of symmetry in physics).
    

  
  

  Online Resources
  

  • Very quick overview of basic terminology and standard examples in group theory 

  A Crash Course In Group Theory

  • Very interesting short article on the history and role of Lie groups

  Sophus Lie and the Role of Lie Groups in Mathematics, by Sigurdur Helgason

  • Representations of finite groups and finite dimensional algebras are treated in a different style in:

  Etingof, P. & Golberg, O. & Hensel, S. & Liu, T. & Schwendner, A. & Vaintrob, D. & Yudovina, E.: Introduction to representation theory. Lecture notes of courses given in the Clay Mathematics Institute and Massachusetts Institute of Technology, 2009. 

  • Representations of Lie algebras are treated also in:

  Shlomo Sternberg: Lie algebras. Online book.
  

  • Lie groups and Lie algebras are treated also in:

  Alexander Kirillov: Introduction to Lie groups and Lie algebras. Online version of a book.

  
  

  • Diaconis, Persi, Group Representations in Probability and Statistics. Book

  • The web page Representation theory online resources lists many more links to freely available books and lecture notes.
    

  
  

  
  

  Sample exam

  The exam of the course Symmetries in 2015 can be found below:

  • an exam of an earlier course