18745. INTRODUCTION TO LIE ALGEBRAS

Tue, Thu 1-2:30, Room 2-135.

Lecturer: George Lusztig

Grader: Aleksandra Utilarova

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 and due the following Tuesday. In late November 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). The Sep.17 lecture is cancelled; instead there will be a lecture on Fri.Sep.20, 4-5 in 2-135. Lecture Notes 1

Lecture Notes 2

Lecture Notes 3

Lecture Notes 4

Lecture Notes 5

Lecture Notes 6

Homework 1, due Sep.10

Homework 2, due Sep.19

Homework 3, due Sep.24

Homework 4, due Oct.1

Homework 5, due Oct.8

Homework 6, due Oct.17

Homework 7, due Oct.22

Homework 8, due Oct.29

Homework 9, due Nov.5

Homework 10, due Nov.12

See M.Geck,On the construction of semisimple Lie algebras and Chevalley groups, Proc.Amer.Math.Soc. 2017, or arxiv:1602.04583

Homework 11, due Nov.19

Homework 12, due Nov.26

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 the end of November.

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