18745. INTRODUCTION TO LIE ALGEBRAS

tue, thu 2:30-4, Room 4-145.

Lecturer: George Lusztig

Grader: Francesco Lin

No textbook is used. Lecture notes will be distributed in class. There will be about 10 problem sets (assigned every Tuesday and due the following Tuesday). On October 17 there will be a one hour quiz. In early December you are supposed to submit a final project on a topic not covered in class. The final grade will be based on problem sets (60/%), quiz (20%), final project(20%). Lecture Notes 1

Lecture Notes 2

Lecture Notes 3

Lecture Notes 3A

Lecture Notes 4

Lecture Notes 5

Homework 1, due Sep.16

Homework 2, due Sep.24

Homework 3, due Oct.1

Homework 4, due Oct.8.

Homework 5, due Oct.22.

Homework 6, due Oct.29.

Homework 7, due Nov.5.

Homework 8, due Nov.12.

Homework 9, due Nov.19.

Homework 10, due Nov.26.

Possible topics for the quiz of Oct.17.

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 leme 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 Dec.8.

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