Math 427: Lie groups
Basic Information
- Instructor: Eugene Lerman
- e-mail:lerman@math.uiuc.edu
- Homepage:
http://www.math.uiuc.edu/~lerman
- Course page:
http://www.math.uiuc.edu/~lerman/427/427syl.html
- Office: 334 Illini Hall
Phone: 244-9510
- Class meets: MWF 9 am
in 155 Altgeld Hall
- Office hours: MW 11-12 and by appointment
Prerequisites
Mathematics 423 or consent of instructor.
If you have any questions or concerns, please contact me by e-mail.
Course outline
This course is an introduction to Lie theory. The first part of the
course will cover the foundations:
- Examples of Lie groups and their Lie algebras
- Homomorphisms
- Lie subgroups
- Covering spaces
- Closed subgroups
- Continuous homomorphisms
- The exponential map
- Representations; the adjoint and coadjoint representations
- Homogeneous manifolds
- Group actions, orbits, adjoint and coadjoint orbits
The remainder of the course will touch on the following topics:
Abelian, nilpotent, solvable and semi-simple Lie groups, Levi
decomposition, semi-direct products. Compact Lie groups, Peter-Weyl
theorem, maximal tori, Weyl groups. Ado's theorem: every finite
dimensional Lie algebra is a matrix Lie algebra. Cartan's theorem
(Lie's third theorem): every finite dimensional Lie algebra is a Lie
algebra of a Lie group.
Texts
The official text is Lie groups beyond an
introduction by A. W. Knapp
There is also a recommended text:
- Lie groups, Lie algebras, and their
representations by V. S. Varadarajan
Grades
The course grade will be based on homework. Homework will be assigned
weekly. One problem per homework will be graded.
Last modified: Tue Aug 24 13:51:30 CDT