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Journal of the London Mathematical Society 1999 59(1):330-344; doi:10.1112/S0024610798006620
© 1999 by London Mathematical Society
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© The London Mathematical Society

A Semigroup Crossed Product Arising in Number Theory

Marcelo Laca and Iain Raeburn

Department of Mathematics, University of Newcastle NSW 2308, Australia. E-mail: marcelo{at}math.newcastle.edu.au
Department of Mathematics, University of Newcastle NSW 2308, Australia. E-mail: iain{at}math.newcastle.edu.au

Received 5 December 1995.

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.


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