Hecke C*-algebras, Schlichting completions, and Morita equivalence

Details Hecke C*-algebras, Schlichting completions, and Morita equivalence Hecke C*-algebras, Schlichting completions, and Morita equivalence

2003-11-13

arxiv.org/abs/math/0311222v5

Mathematics

Operator Algebras

43 pages. Minor revision

Scientific paper

The Hecke algebra H(G,H) of a Hecke pair (G,H) is studied using the Schlichting completion (G',H'), which is a Hecke pair whose Hecke algebra is isomorphic to H(G,H) and which is topologized so that H' is a compact open subgroup of G'. In particular, the representation theory and C*-completions of H(G,H) are addressed in terms of the projection p in C*(G') corresponding to the characteristic function of H', using both Fell's and Rieffel's imprimitivity theorems and the identity H(G,H) = p C_c(G') p. 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 semidirect product) is carried out, and several specific examples are analyzed using this approach.

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