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A Semigroup Crossed Product Arising in Number Theory

Recently Bost and Connes have studied an interesting C*‐algebraic Hecke algebra arising in number theory. Here it is shown that this algebra can be realised as a semigroup crossed product, and be profitably studied using methods developed by the authors for analysing Toeplitz algebras. One main result is a characterisation of faithful representations of the Hecke algebra.