Hecke Algebras of group extensions

Authors

Udo Baumgartner, The University of NewcastleFollow
James Foster, The University of Newcastle
Jacqui Hicks, The University of Newcastle
Helen Lindsay, The University of Newcastle
Benjamin Maloney, University of WollongongFollow
Iain F. Raeburn, University of WollongongFollow
Jacqueline Ramagge, University of WollongongFollow
Sarah Richardson, The University of Newcastle

RIS ID

17586

Publication Details

Baumgartner, U., Foster, J., Hicks, J., Lindsay, H., Maloney, B., Raeburn, I. F., Ramagge, J. & Richardson, S. (2005). Hecke Algebras of group extensions. Communications in Algebra, 33 (11), 4135-4147.

Abstract

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.