Primitive ideals and K-theoretic approach to Bost-Connes systems

By KMS-classification theorem, the Dedekind zeta function is an invariant of Bost-Connes systems. In this paper, we show that it is in fact an invariant of Bost-Connes C⁎-algebras. We examine second maximal primitive ideals of Bost-Connes C⁎-algebras, and apply K-theory to some quotients.