I'm a physics student trying to learn something about the classification of compact simple Lie algebras. I asked one of my TA's for a book recommendation and got Fulton's "Representation Theory". After giving it a shot and reading chapters 7 and 8 (with which's topics I'm already familiar with) I can't really say that I'm understanding a lot. It's hard to say why, but I guess I'm not a huge fan of the way how the author explains (words) things, and I'm missing the mathematical structure (Lemma, Prop., Thm, Proof, etc.).
Googling the topic gives a lot of results, but many of these are semester projects or thesis from other people and not really textbooks. I don't mind reading those, but I'm not really sure if these are the most pedagogical approach to learn something about the topic. Some of the above mentioned semester projects/thesis:
- Classification of Semisimple Lie Algebras, John Austin Charters,
- THE CLASSIFICATION OF SIMPLE COMPLEX LIE ALGEBRAS, Joshua Bosshardt,
- Introduction to Lie Algebras and Representation Theory, Humphreys, J. E..
The last one actually looked quite promising, but I haven't really had time to check it in a bit more detail. My question therefore boils down to: What textbooks/references can you recommend for the topic "Classification of compact simple Lie algebras"?
- I've already had a proper two semester course on representation theory, starting with groups and their properties in a abstract form, then to represenations in general, then to Lie algebra representations, etc. So I have some basic understanding about these things. I saw that in the context of representation theory some concepts of differential geometry are mentioned (manifolds, differentials, etc.), you can also assume that a basic knowledge is present in this area as well.
- I've seen this question, which kind of relates to mine, but it seems to focus on much narrower questions than mine, so I don't really think it qualifies as duplicate.