Lie groups

Instructor

Prof. Paul Gunnells, LGRT 1115L, 413.545.6009, gunnells at math dot umass dot edu. Email to this address is the best way to contact me.

Office Hours

Mondays and Wednesdays, 8:00-9:00, and by appointment.

Overview

A Lie group is a smooth manifold that is a group and such that the group operations (multiplication and inversion) are smooth maps. Their study involves a pleasant mix of geometry, algebra, analysis, and combinatorics.

Outline

The goals of this course are to give an overview of some of the most important aspects of Lie groups, including structure theory and representation theory. I hope that at the end of the course you will have a feel for the mechanics of Lie groups and Lie algebras that show up in "real life," and (more concretely) will know what the characters of representations are and how to compute them.

The course will be divided into three parts.

Resources

Handouts

Textbook

Hall, Brian C. Lie groups, Lie algebras, and representations. An elementary introduction. Graduate Texts in Mathematics 222. Springer-Verlag, New York, 2003. The text is not required (exercises will be assigned separately), but the course will roughly follow its presentation.

Other books

Online references

Lie groups are a central topic; there are many freely available sets of lecture notes floating around. Here are a few I found. I haven't read them, so can't give comments.

Software

Grading

The grades for this course will be based equally on exercises and class participation. As in a previous graduate course, I won't assign individual problem sets, but instead will maintain a list of problems. You can do them at any time during the course; the list will be updated throughout the term (including bugfixes). I would like you to complete 20 problems. Let me know if you find any typos in the problems, or if something isn't clear.


Revised: Wed Apr 23 10:25:11 EDT 2014
Paul Gunnells
gunnells at math dot umass dot edu