2014/12/22 by Takuya Takeishi, Takeishi, Takuya
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Operator Algebras (math.OA) #math.NT #math.OA
paper · pdf · doi:10.48550/arxiv.1412.6900
15 pages. I rewrote Introduction, and I changed section numbers. I corrected several mistakes and did some minor changes
openalex publication_date 2014/12/22 · arxiv created 2015/11/05 · arxiv updated 2015/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 hK1-dimensional irreducible representations and does not have finite-dimensional irreducible representations for the other dimensions, where hK1 is the narrow class number of K. In particular, the narrow class number is an invariant of Bost-Connes C^*-algebras.