## Abstract

A free action α of a group G on a row-finite directed graph E induces an action α_{*} on its Cuntz-Krieger C^{*}-algebra C^{*}(E), and a recent theorem of Kumjian and Pask says that the crossed product C^{*}(E)×_{α*}G is stably isomorphic to the C^{*}-algebra C^{*}(E/G) of the quotient graph. We prove an analogue for free actions of Ore semigroups. The main ingredients are a new generalisation of a theorem of Gross and Tucker, dilation theory for endomorphic actions of Ore semigroups on graphs and C^{*}-algebras, and the Kumjian-Pask Theorem itself.

Original language | English |
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Pages (from-to) | 297-313 |

Number of pages | 17 |

Journal | Journal of Pure and Applied Algebra |

Volume | 159 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 24 May 2001 |

Externally published | Yes |

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