### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*51*(3), 657-695. https://doi.org/10.1017/S0013091506001419

**Hecke C*-algebras, Schlichting completions and Morita equivalence.** / Kaliszewski, Steven; Landstad, Magnus B.; Quigg, John.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 51, no. 3, pp. 657-695. https://doi.org/10.1017/S0013091506001419

}

TY - JOUR

T1 - Hecke C*-algebras, Schlichting completions and Morita equivalence

AU - Kaliszewski, Steven

AU - Landstad, Magnus B.

AU - Quigg, John

PY - 2008/10

Y1 - 2008/10

N2 - 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}=pCcḠp. 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.

AB - 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}=pCcḠp. 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.

KW - Group C-algebra; Morita equivalence

KW - Hecke algebra

KW - Totally disconnected group

UR - http://www.scopus.com/inward/record.url?scp=53449094061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53449094061&partnerID=8YFLogxK

U2 - 10.1017/S0013091506001419

DO - 10.1017/S0013091506001419

M3 - Article

AN - SCOPUS:53449094061

VL - 51

SP - 657

EP - 695

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 3

ER -