## Abstract

The Hecke algebra H of a Hecke pair (G, H) is studied using the Schlichting completion (Ḡ, H), which is a Hecke pair whose Hecke algebra is isomorphic to H and which is topologized so that H̄ is a compact open subgroup of Ḡ. In particular, the representation theory and C*-completions of H are addressed in terms of the projection p=χH C* Ḡ using both Fell's and Rieffel's imprimitivity theorems and the identity H}=pC_{c}Ḡp. An extended analysis of the case where H is contained in a normal subgroup of G (and in particular the case where G is a semi-direct product) is carried out, and several specific examples are analysed using this approach.

Original language | English (US) |
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Pages (from-to) | 657-695 |

Number of pages | 39 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 51 |

Issue number | 3 |

DOIs | |

State | Published - Oct 2008 |

## Keywords

- Group C-algebra; Morita equivalence
- Hecke algebra
- Totally disconnected group

## ASJC Scopus subject areas

- Mathematics(all)