Hecke Algebras of group extensions
We describe the Hecke algebra (Γ,Γ0) of a Hecke pair (Γ,Γ0) in terms of the Hecke pair (N,Γ0) where N is a normal subgroup of Γ containing Γ0. To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S Γ/N satisfies S −1 S = Γ/N, we show that (Γ,Γ0) is the twisted crossed product of (N,Γ0) by S. This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products.
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