The ordered K-theory of a full extension

Details The ordered K-theory of a full extension The ordered K-theory of a full extension

2011-06-08

arxiv.org/abs/1106.1551v1

Mathematics

Operator Algebras

Scientific paper

Let A be a C*-algebra with real rank zero which has the stable weak cancellation property. Let I be an ideal of A such that I is stable and satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a full extension if and only if I is comparable in the lattice of the ideals of A and an appropriate condition on K_0(A) holds. As an immediate application, we extend the classification result for graph C*-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely K-theoretical description of when an essential extension of two simple and stable graph C*-algebras is again a graph C*-algebra.

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