18745. INTRODUCTION TO LIE ALGEBRAS

Tue, Thu 1-2:30, Room 2-136.

Lecturer: George Lusztig

Grader: Dongkwan Kim

Office hour: Thursdays 2:30-3:30.

No textbook is used. Lecture notes will be posted on this website. There will be about 10 problem sets, assigned (almost) every Tuesday y and due the following Tuesday. In early May you are supposed to submit a final project on a topic not covered in class. The final grade will be based on problem sets (70/100), final project(30/100). Lecture Notes 1

Lecture Notes 2

Lecture Notes 3

Lecture Notes 4

Lecture Notes 5

Lecture Notes 6

Homework 1, due Feb.13

Homework 2, due Feb.22

Homework 3, due Feb.27

Homework 4, due March 6

Homework 5, due March 13

Homework 6, due March 20

Homework 7, due Apr.3

Homework 8, due Apr.10

Homework 9, due Apr.24

Homework 10, due May 1

Homework 11, due May 8

Please choose one of the following topics for the final project.

1) The theorem of Levi. 2) The theorem of Ado. 3) Conjugacy of Cartan subalgebras.

(You can consult for example the book: N.Jacobson, Lie Algebras. Note that Jacobson writes functions on the right: xf instead of fx.) If you prefer another topic please let me know. The final project should be a survey of 4 or 5 pages on one of these topics with some (but not all) proofs. Your paper should be given to me by May 10.