Eduardo Ortega: 0-dimensional graph C*-algebras

We will investigate the topological graph C*-algebras \(C^{*}(E) \) with \(E=(E^0,E^1,d,r) \) where \(E^0 \) and \(E^1 \) are 0-dimensional spaces, and see that 0-dimensional topological graphs can be viewed as a dynamical system of a Boolean algebra.

This will allow us to characterize \(C^{*}(E)\) as the universal algebra of the tight representations of certain inverse semigroup, and study properties of \(C^{*}(E)\) from a combinatorial point of view using results of Exel-Pardo.

This is a joint work with Toke Meier Carlsen and Enrique Pardo.