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

Zhuang Niu

*(University of Wyoming)*

3:30 pm to 4:30 pm, May 14th, 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.

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.

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