Classification of C*-algebras generated by representations of the unitriangular group UT(4,Z)UT(4,Z)

It was recently shown that each C*-algebra generated by a faithful irreducible representation of a finitely generated, torsion free nilpotent group is classified by its ordered K-theory. For the three step nilpotent group UT(4,Z)UT(4,Z) we calculate the ordered K-theory of each C*-algebra generated by a faithful irreducible representation of UT(4,Z)UT(4,Z) and see that they are all simple ATAT algebras. We also point out that there are many simple non  -ATAT algebras generated by irreducible representations of nilpotent groups.