Hecke algebras and semigroup crossed product C^∗-algebras

B. Brenken

Vol. 187 (1999), No. 2, 241–262

DOI: 10.2140/pjm.1999.187.241

Abstract

For an almost normal subgroup Γ₀ of a discrete group Γ, conditions are given which allow one to define a universal C^∗-norm on the Hecke algebra H(Γ,Γ₀). If Γ is a semidirect product of a normal subgroup N containing Γ₀ by a group G satisfying some order relations arising from a naturally defined subsemigroup T, and if the normalizer of N is also normal in Γ, then a presentation of H(Γ,Γ₀) is given. In this situation the C^∗-completion of H(Γ,Γ₀) is ∗-isomorphic with the semigroup crossed product C^∗-algebra C^∗(N∕Γ₀) ⋊ T.

Milestones

Published: 1 February 1999