### Abstract

We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a Morita equivalence between the full crossed product and a "universal" fixed-point algebra. We give several applications to Fell bundles over groups, reduced crossed products as fixed-point algebras, and C*-bundles.

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

Pages (from-to) | 1691-1716 |

Number of pages | 26 |

Journal | Indiana University Mathematics Journal |

Volume | 62 |

Issue number | 6 |

DOIs | |

State | Published - 2013 |

### Fingerprint

### Keywords

- Fell bundle
- Groupoid
- Imprimitivity theorem

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indiana University Mathematics Journal*,

*62*(6), 1691-1716. https://doi.org/10.1512/iumj.2013.62.5107

**Fell bundles and imprimitivity theorems : Towards a universal generalized fixed point algebra.** / Kaliszewski, Steven; Muhly, Paul S.; Quigg, John; Williams, Dana P.

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 62, no. 6, pp. 1691-1716. https://doi.org/10.1512/iumj.2013.62.5107

}

TY - JOUR

T1 - Fell bundles and imprimitivity theorems

T2 - Towards a universal generalized fixed point algebra

AU - Kaliszewski, Steven

AU - Muhly, Paul S.

AU - Quigg, John

AU - Williams, Dana P.

PY - 2013

Y1 - 2013

N2 - We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a Morita equivalence between the full crossed product and a "universal" fixed-point algebra. We give several applications to Fell bundles over groups, reduced crossed products as fixed-point algebras, and C*-bundles.

AB - We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a Morita equivalence between the full crossed product and a "universal" fixed-point algebra. We give several applications to Fell bundles over groups, reduced crossed products as fixed-point algebras, and C*-bundles.

KW - Fell bundle

KW - Groupoid

KW - Imprimitivity theorem

UR - http://www.scopus.com/inward/record.url?scp=84904460336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904460336&partnerID=8YFLogxK

U2 - 10.1512/iumj.2013.62.5107

DO - 10.1512/iumj.2013.62.5107

M3 - Article

AN - SCOPUS:84904460336

VL - 62

SP - 1691

EP - 1716

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 6

ER -