thanks very much, it's much clearer now! Just to check that I understood right: the matrix I = (0, -i ; i, 0). is the generator of SO(2) and and it generates SO(2) by taking the exp(-i*f*I) where f is the angle of the rotation in the plane.
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btw: what kind of quantum course are you following that Lie groups are mentioned, but not explained?
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They are just badly explained, because the prof once said she has never had problems in understanding the math, so it's difficult for her to be simple. In addition to that we are supposed to have seen the lie groups and algebras elsewhere, but there already the definition are very different.
