What are the prerequisites for studying Lie theory and which books should I use?

[Saussy]

I have been working on getting the necessary mathematical education to start working on more advanced physics. The need for Lie theory has come up. I already know topology and differential geometry. Are there any other prerequisites to begin studying Lie theory? What books should I look into for the prerequisites and Lie theory itself?

 

[micromass]

Hi Saussy!

I've got two excellent references for you:

• Introduction to Smooth Manifolds by Lee. Fine, this is a differential geometry book, but it has quite a few material on Lee groups and stuff. It won't be comprehensive, but it's certainly worth a look.
• Matrix groups by Baker: you won't need too much differential geometry for this one. Knowing the basic notions is good enough. It also deals a lot with linear algebra and matrices. But it's an excellent reference for Lie groups and Lie algebra's as well!