## Abstract

We analyse Hecke pairs (G,H) and the associated Hecke algebra H when G is a semi-direct product N ⋊ Q and H = M R for subgroups M N and R Q with M normal in N. Our main result shows that, when (G,H) coincides with its Schlichting completion and R is normal in Q, the closure of Hin C*(G) is MoritaRieffel equivalent to a crossed product IQ/R, where I is a certain ideal in the fixed-point algebra C*(N)^{R}. Several concrete examples are given illustrating and applying our techniques, including some involving subgroups of GL(2,K) acting on K^{2}, where K = or K = [p^{1}]. In particular we look at the ax + b group of a quadratic extension of K.

Original language | English (US) |
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Pages (from-to) | 127-153 |

Number of pages | 27 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2009 |

## Keywords

- Group C*-algebra
- Hecke algebra
- Morita equivalence
- Semi-direct product

## ASJC Scopus subject areas

- Mathematics(all)