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

Laca, Marcelo; Raeburn, Iain

J. Lond. Math. Soc., II. Ser. 59, No. 1, 330-344 (1999).

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

Keywords:

covariant representation; \(C^*\)-algebraic Hecke algebra; semigroup crossed product; Toeplitz algebras; faithful representations