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.
- Group C-algebra; Morita equivalence
- Hecke algebra
- Totally disconnected group
ASJC Scopus subject areas