MAT 4144/5158 (Winter 2015)

Introduction to Lie Groups

Official Course Description

Linear groups: the exponential map, Lie correspondence. Homomorphisms and coverings. Closed subgroups. Classical groups: Cartan subgroups, fundamental groups. Manifolds. Homogeneous spaces. General Lie groups.

Prerequisites

The prerequisites for MAT 4144 are MAT 2143, MAT 3120, and MAT 3141. There are no official prerequisites for MAT 5158 but students should take a look at the course descriptions of the MAT 4144 prerequisites and make sure they are familiar with the material covered in those courses.

Course Texts

  • John Stillwell, Naive Lie Theory, Springer, 2008. ISBN: 978-0-387-78214-0 (Print) 978-0-387-78215-7 (Online)
    While on campus (connected to the university network), this book is available for free download here.
  • Brian C. Hall, Lie groups, Lie algebras, and representations, Springer, 2003. ISBN: ISBN: 978-1-4419-2313-4 (Print) 978-0-387-21554-9 (Online)
    While on campus (connected to the university network), this book is available for free download here.

Lecture Notes

Below are lecture notes for the course. They are a single file that will be updated as the course progresses. Please keep in mind that these are notes that I write for myself when preparing the lecture and should be complemented by a student's own class notes. I will often say more in class than is in the notes.

Course Outline

A more detailed syllabus can be found here. This course is cross-listed as an undergraduate course (MAT 4144) and a graduate course (MAT 5158). Students enrolled in MAT 5158 will be expected to do some supplementary reading outside of class and will be asked to solve more advanced problems on the assignments. The exams for the two courses may also differ.

Course Webpage

There are two main online locations for information regarding the course:

  • https://alistairsavage.ca/mat4144. This is the course home page. It will be updated regularly and contains important material for the course. Announcements will also be posted here.
  • Blackboard Learn. Students can access their grades via Blackboard Learn.