Does anyone know of a good introductory text on Lie groups? Will I understand it with only a basic knowledge of topology and no knowledge of differential geometry?
Name:
Sophus Leek2008-05-15 13:03
Funny, I was going to ask the same thing.
I went to the library and took a bunch of Lie groups books off the shelf, looked at each one for five minutes, and put most of them back.
One of the ones I didn't put back was:
Belinfante, Johan G. F. Survey of Lie groups and Lie algebras with applications and computational methods
This isn't going to give anyone a deep or thorough understanding of Lie groups, but it's a really clearly-written overview of what's going on and why it's interesting. I'm partway through and I think having read it will be a big help when I dive into the subject for real.
When I do dive in for real, I'll probably use:
Varadarajan, V. S. Lie groups, Lie algebras, and their representations
My suggestion is that you do what I did: go to the library, take 6-8 books off the shelf whose titles seem to promise the right things ("Introduction to Lie Groups", "Basics of Lie Groups", "A First Course in Lie Groups", etc.) and then look at the introduction and first chapter of each one, for a few minutes each. Then put back all but the two you like best.