MAT 552: Introduction to Lie Groups and Lie Algebras
About the course
Summary. We will go over the fundamental theory of Lie groups and Lie algebras, including the classification of complex semisimple Lie algebras, and some basic facts about their representation theory.
Grading. Grades will be based on weekly homework assignments, class participation, and on a 20-minute presentation towards the end of the semester. Please consult me for possible topics. There is no final exam.
Textbook. We will cover most of the material in the book An Introduction to Lie Groups and Lie Algebras" by Sasha Kirillov. See Appendix B in the book for a tentative syllabus.
Time and location
We meet on Monday and Wednesday afternoon from 2:30–3:50 pm, in Physics P–122 . My office is Math Tower 3–117; office hours are Friday 10am to 12pm.
Homework assignments
- Homework 1 (due February 10): 2.1–3, 2.5, 2.6, 2.8–10, 2.12
- Homework 2 (due February 26): 3.5–6, 3.13, 3.15, 3.18–19 (these two are not in the PDF version)
- Homework 3 (due March 11): 4.1–3, 4.6–7, 4.10
- Homework 4 (due April 3): 5.1–6
- Homework 5 (due April 17): 6.1–5
- Homework 6 (due May 1): 7.1–3, 7.8, 7.12, 7.15, 7.17
Note: I have updated the link above; now the exercises in the printed version and in the PDF version should be the same.
Lecture notes (starting from March 30)
- April 1
- April 6
- April 8
- April 13
- April 15
- April 20
- April 22
- April 27
- April 29
- March 30
- May 4
- May 6
- The classification of root systems (by Maris Ozols)
Policy Statements
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Critical Incident Management. Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students’ ability to learn.