K-Theory and Finiteness

Abstract

In this chapter, we give a discussion of the basics of K-theory for C^*-algebras, as well as properties related to finiteness in C^*-algebras, including the important notion of quasidiagonality, which may be regarded as a type of strong finiteness. Another strong notion of finiteness, stable rank one, is included in a general discussion of stable rank. K-Theory is a vast subject (other parts of the theory are described more comprehensively in [CST04]), and we concentrate only on those aspects directly related to the structure and classi.cation of C^*-algebras, most notably ordered K-theory for finite C^*-algebras; thus the topics treated in this chapter have a natural unity from this point of view.