lie groups are continuous groups.
Classical Lie group:
1. group multiplication = matrix multiplication
2. members: S0(n), O(n), GL(n, Complex), GL(n, Real), SL(n, Complex), SL(n, Real), U(n), SU(n)
S0(2) = rotational symmetry of a circle.
U(1) = phase matrix. Isomorphic to SO(2).
O(2) = reflections and rotations of a circle.
GL(1,C)=g(t,th)=e^(t+ith) 0<=th<2Pi, -infinity