K-Theory for AF Algebras

Abstract

K-theory for C*-algebras provides a means ofestablishing stable and complete*-isomorphism invariants.This work reestablishes the results of Elliot, Dixmier, Bratteli andElliot pertaining to the formation of a complete *-isomorphisminvariants for the class of AF algebras utilizing the K0 functor.It is shown that AF algebras have real rank zero which is the non-commutativeanalogue of zero dimensionality ergo characterizing AF algebras isa first step to characterizing stably finite C*-algebrasin general. The next stage utilizes the K1 functor as a *-isomorphisminvariant between C*-algebras built on one dimensionalspaces such as Bunce Deddens algebras. Such algebras can be viewedas functions on "non-commutative'' spaces giving rise to the fieldof noncommutative topology.