Hecke C*-algebras, Schlichting completions and Morita equivalence

Steven Kaliszewski, Magnus B. Landstad, John Quigg

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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}=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.

Original languageEnglish (US)
Pages (from-to)657-695
Number of pages39
JournalProceedings of the Edinburgh Mathematical Society
Volume51
Issue number3
DOIs
StatePublished - Oct 1 2008

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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