We complete the classification of Bost-Connes systems. We show that two Bost-Connes C*-algebras for number fields are isomorphic if and only if the original semigroups actions are conjugate. Together with recent reconstruction results in number theory by Cornelissen-de Smit-Li-Marcolli-Smit, we conclude that two Bost-Connes C*-algebras are isomorphic if and only if the original number fields are isomorphic.
In this paper, we show that if E is a Fell bundle over an amenablé etale locally compact Hausdorff groupoid such that every fiber on the unit space is nuclear, then C * r (E) is also nuclear. In order to show this result, we introduce (minimal) tensor products of Fell bundles with fixed C * -algebras.
Abstract. The classification problem of Bost-Connes systems was studied by Cornellissen and Marcolli partially, but still remains unsolved. In this paper, we will give a representation-theoretic approach to this problem. We generalize the result of Laca and Raeburn, which concerns with the primitive ideal space on the Bost-Connes system for Q. As a consequence, the Bost-Connes C *
The classification problem of Bost-Connes systems was studied by Cornellissen and Marcolli partially, but still remains unsolved. In this paper, we will give a representation-theoretic approach to this problem. We generalize the result of Laca and Raeburn, which concerns with the primitive ideal space on the Bost-Connes system for Q. As a consequence, the Bost-Connes C *algebra for a number field K has h 1 K -dimensional irreducible representations and does not have finite-dimensional irreducible representations for the other dimensions, where h 1 K is the narrow class number of K. In particular, the narrow class number is an invariant of Bost-Connes C * -algebras.
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