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The ideal structure of the Hecke C*-algebra of Bost and Connes

Marcelo Laca·Iain Raeburn
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Abstract

We compute explicitly the primitive ideal space of the Bost-Connes Hecke C*-algebra by embedding it as a full corner in a transformation group C*-algebra and applying a general theorem of Williams. This requires the computation of the quasi-orbit space for the action of the multiplicative positive rationals on the space of finite adeles. We then carry out a similar computation for the action of the nonzero rationals on the space of full adeles.

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Marcelo Laca, Iain Raeburn. 1999-11-18. The ideal structure of the Hecke C*-algebra of Bost and Connes. https://arxiv.org/abs/math/9911134

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