2008
DOI: 10.1017/s0013091506001419
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Hecke C*-Algebras, Schlichting Completions and Morita Equivalence

Abstract: The Hecke algebra of a Hecke pair (G, H) is studied using the Schlichting completion (Ḡ, ), which is a Hecke pair whose Hecke algebra is isomorphic to and which is topologized so that is a compact open subgroup of Ḡ. In particular, the representation theory and C*-completions of are addressed in terms of the projection using both Fell's and Rieffel's imprimitivity theorems and the identity . An extended analysis of the case where H is contained in a normal subgroup of G (and in particular the case where G… Show more

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Cited by 25 publications
(131 citation statements)
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“…We shall obtain crossedproduct C * -algebras which are Morita-Rieffel equivalent to the completion of the Hecke algebra inside C * (G), similarly to certain results of [5]. At the end of the section we shall briefly indicate how our results can be applied if the Hecke pair is incomplete.…”
Section: Hecke Crossed Productsmentioning
confidence: 59%
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“…We shall obtain crossedproduct C * -algebras which are Morita-Rieffel equivalent to the completion of the Hecke algebra inside C * (G), similarly to certain results of [5]. At the end of the section we shall briefly indicate how our results can be applied if the Hecke pair is incomplete.…”
Section: Hecke Crossed Productsmentioning
confidence: 59%
“…We adopt the conventions of [5], which contains more references. A Hecke pair (G, H) comprises a group G and a Hecke subgroup H, i.e., one for which every double coset HxH is a finite union of left cosets {y 1 H, .…”
Section: Preliminariesmentioning
confidence: 99%
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