Lie Algebras
Math 615 - Fall 2022
Announcements
This page contains some information that can be helpful before you register for the course. After the registration, we will be using odtuclass. You should follow odtuclass and check your emails regularly for important announcements during the semester.
Course Objectives
Lie groups and Lie algebras are especially important in the study of group actions on vector spaces. Besides explaining problems in several areas in mathematics, Lie algebras are interesting in their own right. The classification of simple complex Lie algebras is a beautiful application of linear algebra. The aim of this course is to introduce some of the techniques for studying Lie algebras.
Lectures and Office Hour
Lectures: Monday 10:40-12:30 and Thursday 10:40-11:30 in M203.
Office hour: Thursday 9:40-10:30.
Homeworks, Exams and Grading
Homeworks will be assigned on a regular basis and there will be 4-6 homework sets by the end of the semester. There will be one midterm and a final. The time and the method of each exam will be announced later.
Midterm, 30 points - around the 8th week.
Final, 30 points - during the final exam period.
Homework, 40 points.
Homework Policy: You should write your solutions on your own. You are allowed to consult other people's solutions for homework problems, but you must express everything in your own words. If you copy a solution, which is referred to as cheating, you will probably gain nothing and may encounter penalties.
Textbooks and Tentative Course Outline
1) K. Erdmann, M. J. Wildon, Introduction to Lie Algebras. In the first part, we will cover the basic structure theory of complex semi-simple Lie algebras including the classification by root systems and Dynkin diagrams.
2) B. Hall, Lie Groups, Lie Algebras, and Representations. An Elementary Introduction, Second Edition. In the second part, we wil cover the basic representation theory of Lie groups starting with elementary properties and going through the standard results up to Weyl character formula.
Course Readings
1) William Fulton, Joe Harris, Representation theory: a first course.
2) J. E. Humphreys, Introduction to Lie Algebras and Representation Theory.
3) N. Bourbaki, Lie Algebras and Lie Groups.
PARI / GP
The software PARI / GP is very simple to learn and
extremely strong to do computations with.
A note for undergraduate students
If you are an undergraduate student, your CGPA must be higher than 3.00 in order to take this course. If you are willing to take this course, please send me an email before the registration.