- Welcome to the homepage for MATH 5143: Introduction to Lie Algebras!
- Send questions to
**eric.marberg@gmail.com**. - For office hours, send me an email to arrange an appointment.
- For all course logistics, consult the syllabus.

**Lectures:**

- Wed/Fri 1:30PM to 2:50PM, in Room 5564 near Lift 27-28.

**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, especially about Lie groups.

**Schedule:**

- Week 1: Sections 1.1–3.1
- Week 2: Sections 3.1–4.1
- Week 3: Sections 4.2–5.3
- Week 4: Sections 6.1–6.4
- Week 5: Sections 7.1–8.2
- Lecture 9: abstract Jordan decomposition, special linear representations
- Lecture 10: root space decompositions

- Week 6: Sections 8.3–9.4
- Lectures 11 and 12: properties of root spaces
- Lecture 13: abstract root systems

- Week 7: Sections 10.1–10.4
- Lecture 14: rank two root systems and basic properties
- Lecture 15: simple roots and positive roots

- Week 8: Sections 11.1–16.5
- Lecture 16: reducible root systems and Dynkin diagrams
- Lecture 17: classification of irreducible root systems

- Week 9: Sections 17.1–17.5
- Lecture 18: universal enveloping algebras
- Lecture 19: PBW basis and free Lie algebras

- Week 10: Sections 18.1–20.2
- Lecture 20: Serre's theorem, semisimplicity criteria
- Lecture 21: standard cyclic modules

- Week 11: Sections 20.3–22.5
- Lecture 22: constructing standard cyclic modules
- Lecture 23: finite-dimensional modules

- Week 12: Sections 23.1–24.3
- Lecture 24: Harish-Chandra's theorem, Kostant's formula
- Lecture 24: Weyl character formula

**Assignments:**

- Homework 1 due
**Wednesday, 15 February** - Homework 2 due
**Wednesday, 22 February** - Homework 3 due
**Wednesday, 8 March** - Homework 4 due
**Friday, 17 March** - Homework 5 due
**Wednesday, 12 April** - Homework 6 due
**Friday, 21 April** - Homework 7 due
**Friday, 5 May**