Zinovy Reichstein 
Office: 1105 Math Annex 
Phone: 23929 
Email: reichst at math dot ubc dot ca 
James E. Humphreys, Introduction to Lie algebras and representation theory, Springer, 1972. 
Lie theory is the study of continuous groups of tranformations. These groups play an important role in various areas of mathematics, from PDEs to number theory, as well as in physics. Their structure is most easily understood by in studying their ``linear approximations", otherwise known as Lie algebras. This course we will focus on the study of finitedimenional Lie algebras and their representations by algebraic methods. We will discuss nilpotent, solvable, and semisimple Lie algebras as well as universal enveloping algebras. Our ultimate goal will be the classification of simple complex Lie algebras. This material is foundational for many areas of pure mathematics. Our textbook is concise and beautifully written. I plan to follow it closely through much of the term. 
High comfort level with linear algebra. Familiarity with abstract algebra will also be helpful. 
The course mark will be based entirely on homework assignemnts.
I plan to assign 69 problem sets during the term.
Problem Set 1, due Monday, September 21
Problem Set 2, due Monday, September 28
Problem Set 3, due Wednesday, October 14
Problem Set 4, due Wednesday, October 28
