A crossed-product approach to the Cuntz-Li algebras

TL;DR

This paper introduces a new approach to studying Cuntz-Li algebras using C*-dynamical systems and semidirect product groups, providing fresh insights even for known cases.

Contribution

It develops a generalized framework for C*-algebras associated with integral domains, extending the work of Cuntz and Li through a crossed-product perspective.

Findings

New approach to Cuntz-Li algebras using C*-dynamical systems

Extended the class of C*-algebras studied with this method

Provided novel insights even for previously analyzed cases

Abstract

Cuntz and Li have defined a C*-algebra associated to any integral domain, using generators and relations, and proved that it is simple and purely infinite and that it is stably isomorphic to a crossed product of a commutative C*-algebra. We give an approach to a class of C*-algebras containing those studied by Cuntz and Li, using the general theory of C*-dynamical systems associated to certain semidirect product groups. Even for the special case of the Cuntz-Li algebras, our development is new.