Lie Theory    
      Math 70220  
       Spring 2025

Course Information

> The main text we will refer to will be "Introduction to Lie Algebras and Representation Theory", Humphreys. We will cover the first three chapters of Humphreys, and then topics from other chapters as well as topics on infinite dimensional Lie algebras.

> This course meets MWF 10:30--11:20am in DBRT 202 unless it is a Friday, and then we will usually be in DBRT 213 or 214.

> Prof. K. Barron's regular office hours are Tuesdays 3:30pm-4:30pm, and Fridays 12pm-1pm in 276C Hurley, or by appointment. Mondays and Wednesdays immediately after class as well if you grab me right after class.

> Here are some more details on course logistics: -- info-70220.pdf

Announcements

> Final Exam: The Final Exam will be in DBRT 214 on Thursday, May 8 at 10:30am. It will be comprehensive, covering HW 1 -- 7, Chapters I, and II of Humphreys. HW 8, and Chapter III will not be on the exam.

> Extra Office Hours: There will be Extra Office hours as follows
Friday, May 2nd, 12pm-2pm (for both Prof. Barron's classes), and after 2pm if needed.
Tuesday, May 6th, 12pm-2pm.
Wednesday, May 7th, 12pm-2pm.

> HW 7: HW 7 is available for you to pick up in the math department mailroom.

Homework -- We will have approximately bi-weekly homework assignments. Homework will account for approximately 22% of your grade.

> Homework 1 is due Friday, January 24th: hw1-lie.pdf
> Homework 2 is due Friday, February 7th: hw2-lie.pdf
> Homework 3 is due Friday, February 21th: : hw3-lie.pdf
> Homework 4 is due Friday, March 7th: hw4-lie.pdf
> Homework 5 is due Friday, March 21st: hw5-lie.pdf
> Homework 6 is due Friday, April 4th: hw6-lie.pdf
> Homework 7 is due Friday, April 25th: hw7-lie.pdf
> Homework 8 is due Wednesday, April 30th: hw8-lie.pdf. Note that this homework is for extra credit and the material will not be on the Final Exam. However, you are strongly encouraged to do it to round out your understanding of the classification of finite dimensional semi-simple Lie algebras.
Also note that there was a typo in #2 that was fixed on 4/30, in that phi(z) = mu z.

Exams
Midterms: We will have two midterm exams which will be administered outside of class time. These assessments will count for approximately 44% of your grade.

> Midterm Exam 1 is scheduled for the week of February 24th.
> Midterm Exam 2 is scheduled for Tuesday, April 15th.

Final Exam: The Final Exam will count for approximately 33% of your grade. It will be on Thursday, May 8, 10:30am-12:30pm in DBRT 214 and will be comprehensive, covering HW 1 -- 7, Chapters I, and II of Humphreys. HW 8, and Chapter III will not be on the exam.

Class schedule -- Below I will maintain a rough schedule of what we have covered in Humphreys and what we are about to cover.

Week Dates Sections covered
1 13, 15, 17 Jan.
 Introduction and Chapter I, Section 1
2

22, 24 Jan.

Chapter I, Sections 1 & 2
3 27, 29, 31 Jan.
Chapter I, Sections 2 & 3
4 3, 5, 7 Feb.
Chapter I, Section 3
5 10, 12, 14 Feb.
Chapter I, Section 3 & Chapter II, Section 4
6 17, 19, 21 Feb.
 Chapter II, Section 4
7 24, 26, 28 Feb.
Chapter II, Sections 4 & 5, & Exam I
8 3, 5, 7 Mar.
Chapter II, Sections 5 & 6
10-14 Mar.
SPRING BREAK!!
9 17, 19, 21 Mar.
 Chapter II, Section 6
10 24, 26, 28 Mar.
 Chapter II, Section 6
11 31 Mar., 2 Apr.
Chapter II, Sections 7 & 8.
12 7, 9, 11 Apr.
Chapter II, Section 8.
13 14, 16 Apr.
Chapter II, Section 8 & Exam II & start of Easter Break!
14 23, 25 Apr.
End of Easter Break & Chapter II Section 8 & Chapter III Section 9
15 28, 30 Apr.
 Chapter III Sections 9, 10 & 11.
8 May
 Final Exam at 10:30am in DBRT 214.



Last updated May 2, 2025.