Hecke C*-algebras, Schlichting completions and Morita equivalence

Steven Kaliszewski; Magnus B. Landstad; John Quigg

doi:10.1017/S0013091506001419

Hecke C*-algebras, Schlichting completions and Morita equivalence

Steven Kaliszewski, Magnus B. Landstad, John Quigg

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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_cḠp. 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	https://doi.org/10.1017/S0013091506001419
State	Published - Oct 2008

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S0013091506001419

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title = "Hecke C*-algebras, Schlichting completions and Morita equivalence",

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 {\=H} 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.",

keywords = "Group C-algebra; Morita equivalence, Hecke algebra, Totally disconnected group",

author = "Steven Kaliszewski and Landstad, {Magnus B.} and John Quigg",

note = "Funding Information: Acknowledgements. The early stages of this research were conducted while the authors visited the University of Newcastle, and they thank their host, Iain Raeburn, for his hospitality and helpful conversations. J.Q. acknowledges the support of the Norwegian University of Science and Technology during his visit to Trondheim. All three authors are also grateful for the support of the Centre for Advanced Study in Oslo, and for helpful conversations with Marcelo Laca, Nadia Larsen and George Willis. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

year = "2008",

month = oct,

doi = "10.1017/S0013091506001419",

language = "English (US)",

volume = "51",

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AU - Kaliszewski, Steven

AU - Landstad, Magnus B.

AU - Quigg, John

N1 - Funding Information: Acknowledgements. The early stages of this research were conducted while the authors visited the University of Newcastle, and they thank their host, Iain Raeburn, for his hospitality and helpful conversations. J.Q. acknowledges the support of the Norwegian University of Science and Technology during his visit to Trondheim. All three authors are also grateful for the support of the Centre for Advanced Study in Oslo, and for helpful conversations with Marcelo Laca, Nadia Larsen and George Willis. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

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

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Hecke C*-algebras, Schlichting completions and Morita equivalence

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Keywords

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