MAT 552  Introduction to Lie Groups & Lie Algebras Spring 2021  TΘ 9:45--11:05 am via Zoom

Prof. Claude LeBrun

Office hours: TΘ 1:00-2:30 pm, via Zoom.

This course will offer a one-semester introduction to Lie groups and their Lie algebras. Our approach will emphasize differential-geometric ideas, and will reveal that many algebraic aspects of the subject are intimately related to the geometry of a special class of Riemannian manifolds called symmetric spaces. One main goal of the course will be to understand the classification of compact Lie groups, and much of our time will be spent on the closely-related problem of classifying semi-simple Lie algebras.

Except by explicit permission of the mathematics graduate program director, enrollment in the course is strictly limited to graduate students who have passed either the comprehensive exam or the department's entire suite of first-year graduate core-courses. A basic knowledge of groups, multilinear algebra, and differentiable manifolds will be thus be assumed from the outset. However, the lectures will attempt to be self-contained in all other respects.

Three homework sets will be assigned, collected, and graded during the semester. These will consist of problems posted on this web-site, rather than being drawn directly from a textbook. Your course grade will be based on your homework and class participation.

Optional textbook: Sigurdur Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces. Available editions include AP 1978 & AMS 2012 (pictured).

Alternative textbook: Alexander Kirillov, Jr. An Introduction to Lie Groups and Lie Algebras. Paperback edition. Cambridge UP, 2008.

Homework assignments and other useful information regarding the course will be posted on this web-site.

You may e-mail Prof. LeBrun by This is the best method for making appointments outside normal office hours.

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