GL == general linear group.
GL(1,C)=g(t,th)=e^(t+ith) 0<=th<2Pi, -infinity characters linearly independent.
=> lie algebra with [X(ab),X(gd)]=delta(b,g)Xad-delta(a,d)Xbg
Note that:
Sum(a,Xaa)=Id
GL(n,C) is related to SL(n,C) in the following way:
Let X be a general matrix of GL.
define X~=Xab-1/n*delta(a,b)Id => Tr(X~ab)=0