Partial dynamical systems and AF C*-algebras
By utilizing the connections between C*-algebras, groupoids, and inverse semigroups, we obtain a characterization theorem, in terms of dynamical systems, of approximately finite-dimensional (AF) C*-algebras. The dynamical systems considered in this characterization consist of partially defined homeomorphisms, and our theorem is applied to obtain a result about crossed product C*-algebras. The ideas developed here are then used to compute the K-theory for AF algebras, and these K-theoretic calculations are applied to some specific examples of AF algebras. Finally, we show that for a given dimension group, a groupoid can be obtained directly from the dimension group's structure whose associated C*-algebra has K0 group isomorphic to the original dimension group.