According to https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory:
Yang–Mills theory is a gauge theory based on [...] any compact, semi-simple Lie group.
But the symmetry group of Standard Model, i.e. ${SU(3)}\times{SU(2)}\times{U(1)}$, is not semisimple, due to the $U(1)$ factor, right? What am I missing here?
