### 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 sixterm 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 investigation have more than one ideal and where there are currently no relevant classification theories available.

Original language | English |
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Pages (from-to) | 3811-3847 |

Number of pages | 37 |

Journal | Transactions of the American Mathematical Society |

Volume | 368 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2016 Jun 1 |

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### Keywords

- C*-algebras
- Classification
- K-theory
- Range of invariant
- Six-term exact sequence

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*368*(6), 3811-3847. https://doi.org/10.1090/tran/6443