K-Theory for AF Algebras
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Authors
Ledbetter, Blane M.
Issue Date
2014
Type
Thesis
Language
Keywords
AF algebras , Bunce Deddens algebras , C*-algebras , K-theory
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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.
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In Copyright(All Rights Reserved)