K-theory of C^*-algebras from one-dimensional generalized solenoids

TL;DR

This paper computes the K-theory of C*-algebras derived from one-dimensional generalized solenoids, revealing their structure as one-dimensional generalizations of Cuntz-Krieger algebras.

Contribution

It provides the first explicit computation of K-groups for these C*-algebras, establishing their relation to Cuntz-Krieger algebras.

Findings

K-groups of the C*-algebras are explicitly computed.

Ruelle algebras from these solenoids are identified as generalizations of Cuntz-Krieger algebras.

The structure of these algebras is characterized in terms of their K-theory.

Abstract

We compute the K-groups of C^*-algebras arising from one-dimensional generalized solenoids. The results show that Ruelle algebras from one-dimensional generalized solenoids are one-dimensional generalizations of Cuntz-Krieger algebras.