Summary: Math 7290 Fall 2007
Lie Algebras P. Achar
Office: 266 Lockett Hall
Office hours: Tues. 2:00pm3:30pm or by appointment
Overview. Lie algebras are essential in many areas of mathematics and theoretical physics. In this course,
after covering the definition and basic properties of Lie algebras, we will study the structure theory of
semisimple Lie algebras and the classification of simple Lie algebras, and then take a brief look at their
representation theory. Throughout the course, we'll keep in mind the example of sl2, the smallest semisimple
Lie algebra. It's small enough (only 3-dimensional) to easily do explicit calculations in, and at the same
time interesting enough to give us a good idea of what goes on in higher-dimensional Lie algebras.
Textbook. For much of the semester, we will work from a set of notes by Anthony Henderson. These are
available in PDF format on the Blackboard page for the course. Important: The author has requested that
these notes not be made publicly available. In other words, don't post the PDF file on your own webpage.
At various points in the semester, I will distribute supplementary notes from other sources.
Course outline. A tentative list of topics for the semester is as follows:
Definition and basic properties (Chapters 13) 1 week
Modules and Representations; sl2 (Chapters 46) 2 weeks