K-groups and classification of simple quotients of group C*-algebras of certain discrete 5-dimensional nilpotent groups

The K-groups, the range of trace on K 0, and isomorphism classifications are obtained for simple infinite dimensional quotient C*-algebras of the group C*-algebras of six lattice subgroups, corresponding to each of the six non-isomorphic 5-dimensional connected, simply connected, nilpotent Lie groups. 'Connes non-commutative geometry involving cyclic cocycles and the Chern character play a key role in the proofs.