Math 410
Lie Theory

Progression and homework

Wk	Date	Topics	Documents
1	8/31	Introduction: Lie groups and Lie algebras
2	9/05	Review of linear algebra	Notes on linear algebra
	9/07	Review of linear algebra
3	9/12	Lie algebras: definitions	Notes on Chapter 2
	9/14	Lie algebras: examples and basic manipulations	Homework 1
4	9/19	Isomorphism theorems
	9/21	The adjoint representation, simple Lie algebras	Notes on Chapter 3
5	9/26	Solvable Lie algebras	Homework 2
	9/28	Lie's Theorem	Notes on Chapter 4
6	10/03	Nilpotent Lie algebras	Homework 3
	10/05	Engel's Theorem	Notes on Chapter 5
7	10/10	The Killing form
	10/12	Fall Break - No lecture
8	10/17	Cartan's criterion for solvability	Notes on Chapter 6
	10/19	Midterm examination
9	10/24	Cartan's criterion for semisimplicity
	10/26	Structure of semisimple algebras
10	10/31	Elements of representation theory	Homework 4
	11/02	Complete reducibility, Schur's Lemma	Notes on Chapter 7
11	11/07	Election Day - No lecture
	11/09	Cartan subalgebras
12	11/14	Root space decompositions, I	Notes on Chapter 8
	11/16	Root space decompositions, II
		Thanksgiving Break
13	11/28	Classical simple Lie algebras	Homework 5
	11/30	Abstract root systems
14	12/07	Classification of root systems, I	Notes on the classification
	12/09	Classification of root systems, II
🎓	Dec. 12	Final examination