There's a course on Lie Groups that I'd like to take, but it seems that for various reasons it's a good idea to take Lie algebras along with it. But after having a brief look at the contents of the courses, I found that Lie Groups focus on the interplay between algebras and calculus (well, manifolds and stuff) while Lie algebra is much more heavily centered on abstract algebra.
While I do think ideas involved in both subjects are interesting, the problem is my algebraic background is very weak: I only know of basics of rings, groups, linear algebra and non regarding representation theory. The course states explicitly that knowledge of representation theory is needed, and having a brief look at the lecture notes it does seem to use representation of lie algebra a lot.
I fear that
- My background (especially on representation theory) is too weak
- In terms of exam performance, I'm worried whether this weakness might affect my overall performance.
So I'd like to know:
- Is it possible to have decent understanding in the subject without much knowledge of representation theory?
PS: The reason I want to study Lie theory is mainly for my interest in differential geometry