Irreducible representations of Bost–Connes systems
Takuya Takeishi
University of Tokyo, Japan
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Abstract
The classification problem of Bost–Connes systems was studied by Cornelissen and Marcolli partially, but still remains unsolved. In this paper, we give a representation-theoretic approach to this problem. We generalize the result of Laca and Raeburn, which is concerned with the primitive ideal space of the Bost–Connes system for . As a consequence, the Bost–Connes -algebra for a number field has -dimensional irreducible representations and does not have finite-dimensional irreducible representations for the other dimensions, where is the narrow class number of . In particular, the narrow class number is an invariant of Bost–Connes -algebras.
Cite this article
Takuya Takeishi, Irreducible representations of Bost–Connes systems. J. Noncommut. Geom. 10 (2016), no. 3, pp. 889–906
DOI 10.4171/JNCG/251