Thanks for your feedback. I have studied Lie groups at the level of "geometrical methods of mathematical physics" by Bernard F. Schutz and "Tensors and Group Theory for Physicists" by Nadir Jeevanjee. I haven't begun studying them more formally. I'm just starting graduate level coursework. So...
Quantum Gravity: "Lie Groups" vs. "Banach Algebras & Spectral Theory"
I'm interested in researching quantum gravity & non-commutative geometry. I am planning to take one math course outside of my physics classes this Fall to help, but can't decide between two: "Lie groups" or "Banach algebras &...