C*-ALGEBRAS GENERATED BY PROJECTIVE REPRESENTATIONS OF FREE NILPOTENT GROUPS

We compute the multipliers (two-cocycles) of the free nilpotent groups of class 2 and rank n and give conditions for simplicity of the corresponding twisted group C*-algebras. These groups are representation groups for Zn and can be considered as a family of generalized Heisenberg groups with higher-dimensional center. Their group C*-algebras are in a natural way isomorphic to continuous fields over T1/2n(n-1) with the noncommutative n-tori as fibers. In this way, the twisted group C*-algebras associated with the free nilpotent groups of class 2 and rank n may be thought of as "second order" noncommutative n-tori.