## A semigroup crossed product arising in number theory.(English)Zbl 0922.46058

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. Our main result is a characterization of faithful representations of the Hecke algebra.
Reviewer: M.Laca (Newcastle)

### MSC:

 46L55 Noncommutative dynamical systems 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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