### Abstract

We give a complete classification of the ideals of the core of the C*-algebras associated with self-similar maps under a certain condition. Any ideal is completely determined by the intersection with the coefficient algebra C(K) of the self-similar set K. The corresponding closed subset of K is described by the singularity structure of the self-similar map. In particular the core is simple if and only if the self-similar map has no branch point. A matrix representation of the core is essentially used to prove the classification.

Original language | English |
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Pages (from-to) | 225-255 |

Number of pages | 31 |

Journal | Journal of Operator Theory |

Volume | 75 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 |

### Keywords

- C*-correspondences
- Core
- Ideals
- Self-similar maps

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Kajiwara, T., & Watatani, Y. (2016). Ideals of the core of C*-algebras associated with self-similar maps.

*Journal of Operator Theory*,*75*(1), 225-255. https://doi.org/10.7900/jot.2015feb23.2069