Minimal Bratteli diagrams and dimension groups of AF C*-algebras

Abstract

A method is described which identifies a wide variety of AF algebra dimension groups with groups of continuous functions. Since the continuous functions in these groups have domains which correspond to the set of all infinite paths in what will be called minimal Bratteli diagrams, it becomes possible, in some cases, to analyze the dimension group's order preserving automorphisms by utilizing the topological structure of the associated minimal Bratteli diagram.