The Irreducible Representations Of Noncommutative Dynamical Systems And The Minimal Actions Of The Heisenberg Group On The Cantor Space

In this article,the result of Tomiyama which states that the irreducible unitary equivalence classes of a certain form of representation of the crossed product C*-algebra can determine the orbit of the dynamical systems is weakened to the case of the approximately unitarily equivalence,and shows that it can determine the periodic orbits and the closure of the orbits.At the same time,we investigate the minimal actions of the three-dimensional discrete Heisenberg group on the Cantor space and the structures of the associated C*-algebras.We also compute the K-theory.Finally,we invoke the associated conception in the theory of the(unitary)group representation of infinitely generated nilpotent groups to analysis the representations constructed by Tomiyama,especially the case of the Heisenberg-Cantor dynamical system.