Title

Hecke Algebras of group extensions

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 (N0) 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 (N0) by S. This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products.

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Link to publisher version (DOI)

http://dx.doi.org/10.1080/00927870500261447