On K-theoretic invariants of semigroup C*-algebras attached to number fields, Part II

Abstract: This paper continues the study of K-theoretic invariants for semigroup C*-algebras attached to ax+b-semigroups over rings of algebraic integers in number fields. We show that from the semigroup C*-algebra together with its canonical commutative subalgebra, it is possible to reconstruct the zeta function of the underlying number field as well as its ideal class group (as a group). In addition, we give an alternative interpretation of this result in terms of dynamical systems.