Welcome to the course Lie groups and Lie algebras!

During this course, you will learn about the interconnected topics of Lie groups and Lie algebras. Lie groups are manifolds with a smooth group structure, and Lie algebras are the algebraic structure on their tangent spaces, which can also be studied separately. Examples of Lie groups are given by the real or complex numbers (with addition), the circle S¹ as a subset of the complex numbers (with multiplication), matrix groups such as GL(n), SL(n), O(n), and some rather exotic specimens with strange names such as F₄or E₈. They play an important role as symmetry groups in differential geometry, topology, mathematical physics, and algebraic geometry (by way of their algebraic cousins, algebraic groups). Lie algebras are interesting objects in their own right, but in this course we will mainly use them as a means to classify (compact) Lie groups.

We hope that you, by the end of this course, will be able to apply the techniques of Lie groups and Lie algebras to your field of specialization or start a research project within this topic.

Prerequisites: I expect a good grasp of group theory and knowledge of the fundamentals of smooth manifolds.

Examination: tba

Literature: I will mainly follow (parts of) the course notes by P. Etingof (https://ocw.mit.edu/courses/18-745-lie-groups-and-lie-algebras-i-fall-2020/lists/lecture-notes) and by A. Kirillov (https://www.math.stonybrook.edu/~kirillov/mat552/liegroups.pdf). The former are in fact based on the latter.

A detailed lecture-by-lecture plan can be found under the Syllabus tab.

Remember that you must have registered to maintain access to your courses after the web registration period.

Under Assignments, you will find all homework that is due during the course.

A note on AI: Any use of generative AI in writing your homework is considered plagiarism and cheating. Please don't do it.

Grades

You can find your grades on submitted assignments and quizzes under Grades.

Communication

You can find all announcements posted via Announcements. Questions can be directed at Christina or Tilman via email.

Contact information

In this course, you will meet

Tilman Bauer (lecturer, KTH), tilmanb@kth.se
Christina Kapatsori (TA, KTH), chrkap@kth.se