Hilbert modules over C*-dynamical systems
by
Andrew Toms
York University

The Cuntz semigroup has recently received much attention as an invariant for nuclear separable C*-algebras. One consequence of this study has been the discovery that isomorphism classes of Hilbert modules over such algebras can, in the setting of stable rank one, be classified by the Cuntz semigroup. When the natural partial order on the Cuntz semigroup is determined by states, this classification can be realised in terms of K-theory and traces. We show that the order on the Cuntz semigroup is so determined for the C*-algebras associated to minimal diffeomorphisms.

Date received: April 21, 2008