Representation Theory of Finite Groups

Fall 2006 Math 690Q

 

Instructor:     Richard Ng

Office:            Carver Hall 466
Phone:            515-294-1016
E-mail:            rng@iastate.edu
Homepage: http://www.math.iastate.edu/rng
Office Hours:  T H  1:10pm-2pm  (or by appointment)

Objective:  This is a topic course to give students an introduction on modules over noncommutative rings and representation theory of finite groups.

 

References:  

  1. Charles Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, John Wiley & Sons, New York-London 1962.

  2. Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42. Springer-Verlag, New York-Heidelberg, 1977.

Course description and Topics: The course will cover an elementary theory of modules which includes tensor product, composition series, completely reducible modules. Semisimple rings and group algebras and their modules are of particular interest in this course. Representations of finite groups will be introduced as modules of group algebras. The course will be self-contained and the following topics are considered to be covered:
  1. Representations and Modules
  2. Semisimple Rings and Group Algebras
  3. Group Characters
  4. Induced Representations and Induced Characters--Brauer's Theorem on Induced Characters
  5. Schur's Theory of Projective Representations.

Grading: The grade is based on homework assignments or  presentations.