### 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 |
---|---|

Pages (from-to) | 225-255 |

Number of pages | 31 |

Journal | Journal of Operator Theory |

Volume | 75 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Operator Theory*,

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

**Ideals of the core of C*-algebras associated with self-similar maps.** / Kajiwara, Tsuyoshi; Watatani, Yasuo.

Research output: Contribution to journal › Article

*Journal of Operator Theory*, vol. 75, no. 1, pp. 225-255. https://doi.org/10.7900/jot.2015feb23.2069

}

TY - JOUR

T1 - Ideals of the core of C*-algebras associated with self-similar maps

AU - Kajiwara, Tsuyoshi

AU - Watatani, Yasuo

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - C-correspondences

KW - Core

KW - Ideals

KW - Self-similar maps

UR - http://www.scopus.com/inward/record.url?scp=84962310735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962310735&partnerID=8YFLogxK

U2 - 10.7900/jot.2015feb23.2069

DO - 10.7900/jot.2015feb23.2069

M3 - Article

AN - SCOPUS:84962310735

VL - 75

SP - 225

EP - 255

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 1

ER -