Relative to the following
Indeed, the modern point of view is that the operator of electric charge is the generator of a U(1) group. The charge quantization condition arises in models of unification if the electromagnetic subgroup is embedded into a semi-simple non-Abelian gauge group of higher rank. In this case, the electric charge generator forms nontrivial commutation relations with all other generators of the gauge group.
I have a few questions:
Could someone explain me why it is important that the gauge group $U(1)$ embedded in the a large gauge group should have non-trivial commutation relations to guarantee charge quantization. Isn't it enough that it should be compactly embedded?
Why does the group has to be semi-simple? Aren't the main Grand Unified Theories that are now considered simple group, like $SO(5)$ or $SO(10)$ ?
And finally: the group has to be non-abelian to embed the groups $SU(2)$ and $SU(3)$ describing the other forces?
'Magnetic Monopoles', Yakov M. Shnir Googlebooks: http://books.google.be/books/about/Magnetic_Monopoles.html?id=g3L8SWx8ulkC&redir_esc=y