### Abstract

We investigate the K-theory of unital UCT Kirchberg algebras QS arising from families S of relatively prime numbers. It is shown that K∗.QS/ is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct C∗-algebra naturally associated to S. The C∗-algebra representing the torsion part is identified with a natural subalgebra AS of QS. For the K-theory of QS, the cardinality of S determines the free part and is also relevant for the torsion part, for which the greatest common divisor gS of fp 1 V p 2 Sg plays a central role as well. In the case where S ≤ 2 or gS = 1 we obtain a complete classification for QS. Our results support the conjecture that AS coincides with pϵSOp. This would lead to a complete classification of QS, and is related to a conjecture about k-graphs.

Original language | English |
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Journal | Ergodic Theory and Dynamical Systems |

Volume | 38 |

Issue number | 3 |

Pages (from-to) | 832-862 |

ISSN | 0143-3857 |

DOIs | |

Publication status | Published - 2018 |

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### Cite this

*Ergodic Theory and Dynamical Systems*,

*38*(3), 832-862. https://doi.org/10.1017/etds.2016.63