Hi! I'm studying Lie Algebras and Lie Groups. I'm using Brian Hall's book, which focuses on matrix lie groups for a start, and I'm loving it. However, I'm really having a hard time connecting what he does with what physicists do (which I never really understood)... Here goes one of my questions - very basic, but very important. It is about how one finds a Lie Algebra given its Lie Group. I believe I understood the method exposed in the book, but I am unable to relate it precisely to what I see done in physics textbooks. Thanks!