### Abstract

A Mauldin-Williams graph M is a generalization of an iterated function system by a directed graph. Its invariant set K plays the role of the self-similar set. We associate a C* -algebra O_{M} (K) with a Mauldin-Williams graph M and the invariant set K, laying emphasis on the singular points. We assume that the underlying graph G has no sinks and no sources. If M satisfies the open set condition in K, and G is irreducible and is not a cyclic permutation, then the associated C*-algebra O_{M} (K) is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the Penrose tilings.

Original language | English |
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Pages (from-to) | 545-560 |

Number of pages | 16 |

Journal | Canadian Mathematical Bulletin |

Volume | 51 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 2008 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Ionescu, M., & Watatani, Y. (2008). C*-algebras associated with Mauldin-Williams graphs.

*Canadian Mathematical Bulletin*,*51*(4), 545-560. https://doi.org/10.4153/CMB-2008-054-0