MATH 5143 (Spring 2026)

• 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:

• Tuesdays and Thursdays from 4:30PM to 5:50PM.
• Location: Room 5566, near Lift 27-28.

Textbook:

• Introduction to Lie Algebras and Representation Theory by Humphreys.

Schedule:

• Week 1:
  • Lecture 1: basic definitions, classical examples
  • Lecture 2: comparison with group theory
• Week 2:
  • Lecture 3: solvable and nilpotent Lie algebras, Engel's theorem
  • Lecture 4: Lie's theorem, Jordan decomposition
• Week 3:
  • (no lectures)
• Week 4:
  • Lecture 5: Cartan's criterion, Killing form
  • Lecture 6: semisimplicity, representation theory basics
• Week 5:
  • Lecture 7: Casimir elements, Weyl's theorem
  • Lecture 8: abstract Jordan decomposition, special linear representations

Assignments:

• You are allowed to use any resources to do the assignments.
  But your solutions must be hand-written and delivered in-person during lecture.
  No electronic submissions.
• Homework 1 due Tuesday, February 24
• Homework 2 due Tuesday, March 3