Constructing AT-algebras from zero-dimensional systems

Assistant Professor Paul Herstedt; Department of Mathematics, Grinnell College

We explain directly how one constructs approximating circle algebras in crossed products from certain zero-dimensional dynamical systems. We explain how one overcomes the problems that one encounters when expanding from the case where the system has no periodic points (e.g. infinite minimal systems) to give a direct proof of the canonical essentially minimal example, the one-point compactification of the integers. Expanding beyond that is a notational nightmare, but it is not hard to intuitively explain.