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Math 7290 Fall 2010 Introduction to Lie Theory P. Achar

Summary: Math 7290 Fall 2010
Introduction to Lie Theory P. Achar
Course Information
Office: 266 Lockett Hall
Phone: 578-7990
E-mail: 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, Springer-Verlag, 2005. On campus, this book is available on-line 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 self-contained course on algebraic geometry over a field


Source: Achar, Pramod - Department of Mathematics, Louisiana State University


Collections: Mathematics