$C^*$-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.
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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