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

2015/03/05 by Li, Xin
#11R29 #46L80 #Dynamical Systems (math.DS) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Operator Algebras (math.OA) #Primary 46L05 #Secondary 11R04

paper · doi:10.48550/arxiv.1503.01708

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.

Related

• On K-theoretic invariants of semigroup C*-algebras attached to number fields
• C*-algebras of Toeplitz type associated with algebraic number fields
• Semigroup C*-algebras of ax+b-semigroups
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• Semigroup C*-algebras and amenability of semigroups