Partial isometries and extensions of AT-algebras

摘要

In this paper, we will define several new isomorphism invariants for C*-algebras by hyponormal partial isometries and discuss the relation between these invariants and K-theory of C*-algebras. This study was in part inspired by the work of H. Lin and H. Su in the context of AT-algebras. An AT-algebra often becomes an extension of an AT-algebra by an AF-algebra. We show that there is an essential extension of a simple AT-algebra which has real rank zero by an AF-algebra such that it has real rank zero and is not an AT-algebra.