Generalised Hecke Algebras and C * -completions
نویسندگان
چکیده
For a Hecke pair (G, H) and a character σ of H we consider a generalised Hecke algebra Hσ(G, H), which we study by embedding the given Hecke pair in a Schlichting completion (Gσ, Hσ) that comes equipped with a continuous extension σ on Hσ. The image of σ in Cc(Gσ) is a non-full projection pσ, and Hσ(G, H) is isomorphic to pσCc(Gσ)pσ. We study the structure and properties of C *-completions of a generalised Hecke algebra arising from this corner realisation, and via Morita-Rieffel equivalence we identify, in some cases explicitly, the resulting proper ideals of C * (Gσ). By letting σ vary, we can compare these ideals. Applications include ax + b-groups and the Heisenberg group.
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