Lie Groups and Lie Algebras

Catalog description

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.