- Welcome to the homepage for MATH 5143: Introduction to Lie Algebras!
- Send questions to
**eric.marberg@gmail.com**or our Discord server. - For office hours, send me an email to arrange an appointment.
- For information about prerequisites, grades, and course content, consult the syllabus.

**Lectures:**

- Tuesdays from 1:30PM to 4:20PM.
- Lectures will be online. Join through the Zoom Meeting link in Canvas.

**Textbooks:**

- Our main textbook is Introduction to Lie Algebras and Representation Theory by Humphreys.
- Some other online textbooks can be found here and here. These include more material than we will cover in this semester, especially about Lie groups.

**Schedule:**

- Lecture 1 : basic definitions, solvable and nilpotent Lie algebras (1.1–3.1)
- Lecture 2 : Engel's and Lie's theorems, Jordan decomposition (3.1–4.2)
- Lecture 3 : Cartan criterion, Killing form, semisimplicity (4.3–5.3)
- Lecture 4 : modules, Casimir element, Weyl's theorem, abstract Jordan decomposition (6.1–6.4)
- Lecture 5 : special linear representations, root space decompositions (7.1–8.2)
- Lecture 6 : properties of root spaces, abstract root systems (8.3–9.4)
- Lecture 7 : properties of simple roots and the Weyl group (10.1–10.4)
- Lecture 8 : classification of irreducible root sytems, isomorphism and conjugacy theorems (11.1–16.5)
- Lecture 9 : universal enveloping algebras (17.1–17.5)
- Lecture 10 : Serre's theorem, weight spaces, standard cyclic modules (18.1–20.2)
- Lecture 11 : finite-dimensional modules, multiplicity formulas, formal characters (20.3–22.5)
- Lecture 12 : Harish-Chandra's theorem, more formal characters, Kostant's formula (23.1–24.2)
- Lecture 13 : Weyl character formula, Chevalley bases (24.3–25.5)

**Assignments:**

- Homework 1 due
**Thursday, 17 February** - Homework 2 due
**Thursday, 24 February** - Homework 3 due
**Thursday, 3 March** - Homework 4 due
**Thursday, 17 March** - Homework 5 due
**Thursday, 24 March** - Homework 6 due
**Thursday, 31 March** - Homework 7 due
**Thursday, 21 April** - Homework 8 due
**Tuesday, 3 May** - Homework 9 due
**Thursday, 17 May**