### Abstract

The first imprimitivity theorems identified the representations of groups or dynamical systems which are induced from representations of a sub-group. Symmetric imprimitivity theorems identify pairs of crossed products by different groups which are Morita equivalent and hence have the same representation theory. Here we consider commuting actions of groups H and K on a C*-algebra which are saturated and proper as defined by Rieffel in 1990. Our main result says that the resulting Morita equivalence of crossed products is natural in the sense that it is compatible with homomorphisms and induction processes.

Original language | English (US) |
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Pages (from-to) | 2319-2327 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 141 |

Issue number | 7 |

DOIs | |

State | Published - Apr 24 2013 |

### Keywords

- Crossed products
- Fixed-point algebras
- Naturality
- Proper actions on C*-algebras
- Symmetric imprimitivity theorem

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

An Huef, A., Kaliszewski, S., Raeburn, I., & Williams, D. P. (2013). Naturality of symmetric imprimitivity theorems.

*Proceedings of the American Mathematical Society*,*141*(7), 2319-2327. https://doi.org/10.1090/S0002-9939-2013-11712-0