Actually while the Lie algebra su(3) x su(2) x u(1) of the standard model is a direct sum of three simple Lie algebras, the gauge group itself appears to be the group S(U(3) x U(2)).

For much more details see the discussion on the web page ''Standard Model Group Structure'' by Tony Smith.

Actually while the Lie algebra $su(3) \oplus su(2) \oplus u(1)$ of the standard model is a direct sum of three simple Lie algebras, the gauge group itself appears to be the group $S(U(3) \times U(2))$.

For much more details see the discussion on the web page ''Standard Model Group Structure'' by Tony Smith.

Actually while the Lie algebra su(3) x su(2) x u(1) of the standard model is a direct product of three simple Lie algebras, the gauge group itself appears to be the group S(U(3) x U(2)).

For much more details see the discussion on the web page ''Standard Model Group Structure'' by Tony Smith.

Actually while the Lie algebra su(3) x su(2) x u(1) of the standard model is a direct sum of three simple Lie algebras, the gauge group itself appears to be the group S(U(3) x U(2)).

For much more details see the discussion on the web page ''Standard Model Group Structure'' by Tony Smith.