Anomaly cancellation and the gauge group of the Standard Model in NCG

It is well known that anomaly cancellation almost determines the hypercharges in the Standard Model. A related (and somewhat more stronger) phenomenon takes place in Connesʹ NCG framework: unimodularity (a technical condition on elements of the algebra) is strictly equivalent to anomaly cancellation; and this in turn reduces the symmetry group of the theory to the standard SU(3) × SU(2) × U(1).