Math 70220
      Spring 2022  

      Lie Algebras

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 11:30am--12:20pm in DBRT 317.
Current mask policy: For now masks are optional but highly recommended. If you are feeling ill at all though or think you may have been exposed to an airborne disease such as COVID or the flu, please get tested and wear your mask or stay home and ask for a recording of class. The COVID-19 levels in the community are very low now, but are rising. There have been students and faculty on campus who have had COVID cases that are not being reported on the ND dashboard and some of these are severe. It is currently highly recommended that you wear a mask. If cases continue at this pace or rise, we will reinstitute a mandatory (rather than recommended) in class mask policy.

> Prof. K. Barron's regular office hours are Monday and Wednesday immediately after class in our classroom, and 2pm-3pm in 276C Hurley, or by appointment. Questions by email are always welcome as well.

Announcements

> We will have extra office hours during the reading period before Final Exams. Please let me know what times might be best.
For now Extra Office hours are:
3pm - 4pm Wednesday, April 27;
3:15pm - 4:15pm Friday, April 29; and
3pm - 4pm Monday, May 2.

Homowork -- We will have approximately bi-weekly homework assignments. They will be posted below as we go along. Homework will account for approximately 35% of your grade.

> Homework 1 is due Wednesday, January 26th: hw1
> Homework 2 is due Wednesday, February 9th: hw2
> Homework 3 is due Wednesday, March 2nd: hw3
> Homework 4 is due Wednesday, March 16th: hw4
> Homework 5 is due Wednesday, April 6th: hw5
> Homework 6 is due Wednesday, April 13th: hw6
> Homework 7 is due Tuesday, April 26th: hw7
> Homework 8 - Extra Credit is due Friday, May 6th: hw8-extra

Quizzes/Exams -- We will have three quizzes/midterm exams which will be administered outside of class time. These assessments will count for approximately 35% of your grade.

> Midterm Exam 1 Thursday, February 17th, Hayes-Healy 117 drop in hours 5pm - 8:15pm.
> Midterm Exam 2 Thursday, March 31th, Hayes-Healy 117 drop in hours 5:30pm - 7:30pm.
> Midterm Exam 3 Thursday, April 21st and Friday, April 22nd.

Final Exam. The Final Exam will count for approximately 30% of your grade. It will be offered at two times:
Monday, May 2nd, 4:15pm - 6:15pm in DBRT 317;
or
Wednesday, May 4th, 10:30am - 12:30pm in Hayes-Healy 229.
.

Class schedule -- This is a rough schedule of what we have covered in Humphreys and what we are about to cover.

Week Dates Sections covered
1 10, 12, 14 Jan.
Introduction and Chapter I, Section 1.
2

19, 21 Jan.

Chapter I, Sections 1 & 2.
3 24, 26, 28 Jan.
Chapter I, Sections 2 & 3.
4 31 Jan., 2, 4 Feb.
Chapter I, Section 3.
5 7, 9, 11 Feb.
Chapter I, Section 3 & Chapter II, Section 4.
6 14, 16, 18 Feb.
Chapter II, Section 4 & Exam I Q&A & Exam I.
7 21, 23, 25 Feb.
Chapter II, Section 4.
8 28 Feb., 2, 4 Mar.
Chapter II, Sections 4 & 5.
Nul 5-13 Mar.
SPRING BREAK!!
9 14, 16, 17 Mar.
Chapter II, Sections 5 & 6.
10 21, 24, 25 Mar.
Chapter II, Sections 6 & 7 -- via
Video on Sakai. No in person class. Sections 6.2, 6.3 and then only 7.1 from video on Chapter 7.
11 28, 30 Mar., 1 Apr.
Chapter II, Sections 7 & 8, & Exam II.
12 4, 6, 8 Apr.
Chapter II, Section 8
13 11, 13 Apr.
Chapter II, Section 8, & Chapter III, Section 9
14 20, 22 Apr.
Exam iii Q&A, & Chapter III, Section 9
15 25, 26 Apr.
Chapter III, Sections 9, 10 & 11




Last updated May 1, 2022.