Partial dynamical systems and AF C*-algebras

Abstract

We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C*-algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by utilizing the actions of these partial homeomorphisms, and these K-theoretic calculations are applied to some specific examples of AF algebras. Finally, we show that, for a certain class of dimension groups, a groupoid can be obtained directly from the dimension group's structure whose associated C*-algebra has K_0 group isomorphic to the original dimension group.