 
Summary: Math 7290 Fall 2010
Introduction to Lie Theory P. Achar
Course Information
Office: 266 Lockett Hall
Phone: 5787990
Email: pramod@math.lsu.edu
Webpage: http://www.math.lsu.edu/~pramod/
Textbook. P. Tauvel and R.W.T. Yu, Lie Algebras and Algebraic Groups, Springer Monographs in Math
ematics, SpringerVerlag, 2005. On campus, this book is available online from Springer at the following
address: http://www.springerlink.com/.
Course outline. The main topic of the course is the structure theory of Lie algebras and algebraic groups
over C, based on chapters 1830 of the textbook. We will proceed roughly according to the following schedule:
Root systems (Chap. 18) 2 weeks
Introduction to Lie algebras (Chap. 1920) 3 weeks
Algebraic groups and their Lie algebras (Chap. 2124) 3 weeks
Structure theory of algebraic groups (Chap. 2528) 3 weeks
Structure and representations of Lie algebras (Chap. 2930) 2 weeks
If there is time remaining at the end of the semester, we may cover additional topics such as nilpotent orbits,
flag varieties, Bruhat decomposition, or the BorelWeilBott theorem.
Note. The first half of the textbook is essentially a selfcontained course on algebraic geometry over a field
