Noncommutative semialgebraic sets in nilpotent variables

We solve the lifting problem in C*-algebras for many sets of relations that include the relations x(j)(Nj) = 0 for all variables. The remaining relations must be of the form vertical bar vertical bar p(x(1,...,)x(n))vertical bar vertical bar <= C for C a positive constant and p a noncommutative *-polynomial that is in some sense homogeneous. For example, we prove liftability for the set of relations x(3) = 0, y(4) = 0, z(5) = 0, xx* vertical bar yy* vertical bar zz* <= 1. Thus we find more noncommutative semialgebraic sets that have the topology of noncommutative absolute retracts.