MAT 4144/5158 (Winter 2010)

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

MAT 4144:

  • John Stillwell, Naive Lie Theory, Springer, 2008. From on-campus computers, this text is available for free download from www.springerlink.com (search for the author's name and then click on the "books" link on the right). This is the text we will generally follow in class.

MAT 5158:

The following texts will be useful for students in MAT 5158 (and perhaps those in MAT 4144 as well). They have been put on reserve at Morisset Library.

  • Wulf Rossmann, Lie Groups: An Introduction Through Linear Groups, Oxford University Press, 2006.
  • Brian C. Hall, Lie groups, Lie algebras, and representations, Springer, 2003. This book is available electronically via the website of the University Library (click on "E-Books", then on "MyiLibrary", and then search for the book).
  • Alexander Kirillov, Introduction to Lie groups and Lie algebras, Cambridge University Press, 2008. A preprint version is available for download from Kirillov's webpage.

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: