The Ranges of K-theoretic Invariants for Nonsimple Graph Algebras

Abstract

There are many classes of nonsimple graph C*-algebras that are classified by the six-term exact sequence in K-theory. In this paper we consider the range of this invariant and determine which cyclic six-term exact sequences can be obtained by various classes of graph C*-algebras. To accomplish this, we establish a general method that allows us to form a graph with a given six-term exact sequence of K-groups by splicing together smaller graphs whose C*-algebras realize portions of the six-term exact sequence. As rather immediate consequences, we obtain the first permanence results for extensions of graph C*-algebras. We are hopeful that the results and methods presented here will also prove useful in more general cases, such as situations where the C*-algebras under investigations have more than one ideal and where there are currently no relevant classification theories available.

40 pages

References in corpus (3)

• The K-theoretical range of Cuntz-Krieger algebras
• The ordered K-theory of a full extension
• Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

Cited by in corpus (2)

• The complete classification of unital graph $C^{\ast }$-algebras: Geometric and strong
• The extension problem for graph $C^{\ast }$-algebras