### Abstract

Consider a projective limit G of finite groups Gn. Fix a compatible family ^{n} of coactions of the Gn on a C^{*}-algebra A. From this data we obtain a coaction of G on A. We show that the coaction crossed product of A by is isomorphic to a direct limit of the coaction crossed products of A by the ^{n}. If A=C^{*}() for some k-graph , and if the coactions ^{n} correspond to skew-products of , then we can say more. We prove that the coaction crossed product of C^{*}() by may be realized as a full corner of the C^{*}-algebra of a (k+1)-graph. We then explore connections with Yeends topological higher-rank graphs and their C^{*}-algebras.

Original language | English (US) |
---|---|

Pages (from-to) | 379-398 |

Number of pages | 20 |

Journal | Journal of the Australian Mathematical Society |

Volume | 86 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

- C*-algebra
- Coaction
- Covering
- Crossed-product
- Graph algebra
- K-graph.

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Australian Mathematical Society*,

*86*(3), 379-398. https://doi.org/10.1017/S144678870800030X

**Coverings of skew-products and crossed products by coactions.** / Pask, David; Quigg, John; Sims, Aidan.

Research output: Contribution to journal › Article

*Journal of the Australian Mathematical Society*, vol. 86, no. 3, pp. 379-398. https://doi.org/10.1017/S144678870800030X

}

TY - JOUR

T1 - Coverings of skew-products and crossed products by coactions

AU - Pask, David

AU - Quigg, John

AU - Sims, Aidan

PY - 2009/6

Y1 - 2009/6

N2 - Consider a projective limit G of finite groups Gn. Fix a compatible family n of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction of G on A. We show that the coaction crossed product of A by is isomorphic to a direct limit of the coaction crossed products of A by the n. If A=C*() for some k-graph , and if the coactions n correspond to skew-products of , then we can say more. We prove that the coaction crossed product of C*() by may be realized as a full corner of the C*-algebra of a (k+1)-graph. We then explore connections with Yeends topological higher-rank graphs and their C*-algebras.

AB - Consider a projective limit G of finite groups Gn. Fix a compatible family n of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction of G on A. We show that the coaction crossed product of A by is isomorphic to a direct limit of the coaction crossed products of A by the n. If A=C*() for some k-graph , and if the coactions n correspond to skew-products of , then we can say more. We prove that the coaction crossed product of C*() by may be realized as a full corner of the C*-algebra of a (k+1)-graph. We then explore connections with Yeends topological higher-rank graphs and their C*-algebras.

KW - C-algebra

KW - Coaction

KW - Covering

KW - Crossed-product

KW - Graph algebra

KW - K-graph.

UR - http://www.scopus.com/inward/record.url?scp=70349199454&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349199454&partnerID=8YFLogxK

U2 - 10.1017/S144678870800030X

DO - 10.1017/S144678870800030X

M3 - Article

AN - SCOPUS:70349199454

VL - 86

SP - 379

EP - 398

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 3

ER -