$C^*$-algebras of certain non-minimal homeomorphisms on a Cantor set -- II

Zhuang Niu  (University of Wyoming)

9:30 am to 10:30 pm, May 22nd, 2013   Science Building A1510

Abstract:

We shall consider a homeomorphism on a Cantor set with finitely many minimal invariant closed subsets (assume none of them are clopen),and consider the crossed-product $C^*$-algebra and certain sub-algebras. It turns out that if the Cantor system has more than two minimal subsets,then the dimension group of the ideal (corresponding to the standard invariant open set) of the Brattteli-Vershik model must contain infinitesimal elements.

Using these infinitesimal elements,a necessary-and-sufficent condition is given on certain(unordered) Bratteli diagrams so that they can be ordered to model Cantor systems with finitely many minimal subset.

This is a joint work with Sergey Bezuglyi and Wei Sun.