Journal of Operator Theory

Volume 50, Issue 1, Summer 2003 pp. 169-178.

Hecke $C^*$-algebras and amenability

Authors: Kroum Tzanev
Author institution: Laboratoire Emile Picard, UPS 118, route de Narbonne, 31062 Toulouse Cedex 4, France

Summary: Following an idea of G.~Schlichting we associate to any Hecke pair of groups a pair consisting of a totally disconnected group and a compact-open subgroup. Using this correspondence we show how the study of Hecke $C^*$-algebras can be reduced to the study of corners in $C^*$-algebras of totally disconnected groups. Afterwards this method is used to study the amenability of Hecke pairs.

Keywords: Hecke algebras, $C^*$-algebras, amenability, almost-normal subgroups

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