MATH 6390
Lie Groups and Lie Algebras
Lie groups, Lie algebras, and their representations play an important role in much of mathematics, particularly in number theory, mathematical physics, and topology. This is an introductory course, meant to be useful for more advanced topics and applications. The relationship between Lie groups and Lie algebras will be highlighted throughout the course. A different viewpoint is that of algebraic groups. We will endeavor to discuss this along with the smooth viewpoint. Some knowledge of differential and algebraic geometry are helpful.
fall 2026
Readings
- Kirillov, Alexander Jr., An Introduction to Lie Groups and Lie Algebras , Cambridge University Press, 2008 (ISBN: 978-0-521-88969-8) — free e-book through the Cornell Math Library
- (optional) Helgason, Sigurdur, Differential Geometry and Symmetric Spaces , American Mathematical Society, 2001 (ISBN: 978-0-821-82735-2) — free e-book through the Cornell Math Library
- (optional) Warner, Frank, Foundations of Differentiable Manifolds and Lie Groups , Springer-Verlag, 1983 (ISBN: 978-0-387-90894-6) — free e-book through the Cornell Math Library
- (optional) Humphreys, James, Introduction to Lie Algebras and Representation Theory , Springer-Verlag, 1972 (ISBN: 0-387-90053-5) — free e-book through the Cornell Math Library
- (optional) Springer, T.A., Linear Algebraic Groups 2nd edition , Birkhauser Boston, 2009 (ISBN: 978-0-8176-4839-8) — free e-book through the Cornell Math Library
Prerequisites & course information
background equivalent to: MATH 4330 and MATH 4340.