Hecke Algebras of Group Extensions |
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| Authors: | Udo Baumgartner James Foster Jacqueline Hicks Helen Lindsay Ben Maloney Iain Raeburn |
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| Institution: | School of Mathematical and Physical Sciences , The University of Newcastle , Callaghan, NSW, Australia |
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| Abstract: | 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. |
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| Keywords: | Hecke algebras Representation Twisted crossed product by semigroups |
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