Efren Ruiz

Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

We prove that ample groupoids with sigma-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matuis notion of Kakutani equivalence. We use this result to show that diagonal-preserving stable isomorphisms of graph C*-algebras or Leavitt path algebras give rise to isomorphisms of the groupoids of the associated stabilised graphs. We deduce that the Leavitt path algebras

Classification of extensions of classifiable C*-algebras

L_Z(E_2)

The Ordered

and

K

L_Z(E_{2-})

-theory of a Full Extension

are not stably *-isomorphic.

On Rørdam's classification of certain

Abstract For a certain class of extensions e : 0 → B → E → A → 0 of C * -algebras in which B and A belong to classifiable classes of C * -algebras, we show that the functor which sends e to its associated six term exact sequence in K-theory and the positive cones of K 0 ( B ) and K 0 ( A ) is a classification functor. We give two independent applications addressing the classification of a class of C * -algebras arising from substitutional shift spaces on one hand and of graph algebras on the other. The former application leads to the answer of a question of Carlsen and the first named author concerning the completeness of stabilized Matsumoto algebras as an invariant of flow equivalence. The latter leads to the first classification result for nonsimple graph C ∗ -algebras.

C^*

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 the extension is stenotic and K-lexicographic. 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.

-algebras with one non-trivial ideal, II

In this paper we extend the classification results obtained by Rordam in the paper [16]. We prove a strong classification theorem for the unital essential extensions of Kirchberg algebras, a classification theorem for the non-stable, non-unital essential extensions of Kirchberg algebras, and we characterize the range in both cases. The invariants are cyclic six term exact sequences together with the class of some unit.

Corners of Cuntz-Krieger algebras

We show that if

Classifying C⁎-algebras with both finite and infinite subquotients

A