ON THE CONSTRUCTION OF SU(N)-X-U(1) MODELS IN A NONCOMMUTATIVE GEOMETRY SETTING

A gauge theory is developed in the framework of non-commutative geomet ry (NCG), the latter exemplified in an A(l,m) bigraded-algebra setting . Symmetries and representations are derived from the general SU(n+1) group, with a glimpse to the case of SU(n/1) supergroups. The ordinary gauge group involved is actually SU(n)xU(1) spontaneously broken down to SU(n-1) by means of a Higgs potential, emerging in the remarkable NCG pattern. The special n=2 case in the A(2,4) algebra is treated in full detail as a prototype for the construction of more realistic mode ls.