The Ranges of K-theoretic Invariants for Nonsimple Graph Algebras

Details The Ranges of K-theoretic Invariants for Nonsimple Graph Algebras The Ranges of K-theoretic Invariants for Nonsimple Graph Algebras

2012-02-09

arxiv.org/abs/1202.1989v1

Mathematics

Operator Algebras

40 pages

Scientific paper

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.

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