MATH 5143 (Spring 2023)
Overview:
- 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:
Schedule:
- Week 1: Sections 1.1–3.1
- Week 2: Sections 3.1–4.1
- Lecture 3: nilpotent Lie algebras, Engel's theorem
- Lecture 4: solvable Lie algebras, Lie's theorem
- Week 3: Sections 4.2–5.3
- Lecture 5: Jordan decomposition, Cartan's criterion
- Lecture 6: Killing form, semisimplicity
- 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
- Week 7: Sections 10.1–10.4
- 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
- Week 10: Sections 18.1–20.2
- Week 11: Sections 20.3–22.5
- Week 12: Sections 23.1–24.3
Assignments: