Math 210C: Lie Groups and Lie Algebras

This course will have three texts:

All three texts are available on-line through the Stanford Libraries. Our main text will be Humphreys, which we will read. However, an important source of Lie theory is Lie groups, so we will also discuss Lie groups in the Lectures. Many important results such as the Weyl character formula apply equally well to representations of Lie groups or Lie algebras, so we will discuss applications to Lie groups as we study Lie algebras.

Lectures

Office Hours

Canvas and Gradescope links

Lecture Notes

The proof in Humphrey's of the Lemma in Section 4.3 (leading to Cartan's criterion) is a little confusing. An alternative version of the proof in this web page of Brian Weber's is less general since it requires the ground field to be $\mathbb{C}$, but I found it helpful:

Homework

Homework will be due on Mondays, and handled through Gradescope.