This course, after a general introduction to Lie groups and Lie algebras, will focus mainly on the theory of compact Lie groups: Their structure theory, representations, and classi cations.

It can also be shown that for every finite-dimensional Lie algebra, g, there is a connected and simply connected Lie group, G, such that g is the Lie algebra of G.

Math 508 – Lie Algebras (lecture notes) Instructor: Julia Pevtsova Winter 2023. Contents.

The functor G 7!Lie(G) gives an equivalence of categories between the category scLieGp of simply-connected Lie groups (over R or C) and the category LieAlg of nite-dimensional Lie …

May 29, 2016 · We’ll classify the simple Lie algebras, which ends up using the fundamental objects called root systems. Root systems are so fundamental to math that this course might …

We show how Lie group representations give rise to Lie algebra representations, and vice-versa. We also introduce the universal enveloping algebra of a Lie algebra.

ventually see how to reconstruct g. We'll see that to every root system there corresponds a semisimple Lie algebra, so it's imp. rtant to know all the root systems. Last time we saw the …