K-theory for ring C*-algebras - the case of number fields with higher roots of unity

TL;DR

This paper calculates the K-theory of ring C*-algebras associated with rings of integers in number fields, especially those with higher roots of unity, providing a comprehensive understanding of their algebraic structure.

Contribution

It extends the computation of K-theory for ring C*-algebras to include cases with higher roots of unity in arbitrary number fields, filling a significant gap in the field.

Findings

Complete determination of K-theory for ring C*-algebras in these cases

Explicit formulas for K-groups involving higher roots of unity

Unified approach applicable to all number fields

Abstract

We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.