Ring C*-algebras

TL;DR

This paper introduces a new class of C*-algebras constructed from arbitrary rings, analyzing their structure and conditions for simplicity and pure infiniteness, motivated by algebraic number theory.

Contribution

It defines ring C*-algebras for arbitrary rings and characterizes their structural properties, including simplicity and pure infiniteness, with various examples.

Findings

Conditions for ring C*-algebras to be purely infinite and simple

Construction of reduced and full ring C*-algebras

Examples illustrating the theory

Abstract

We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples. Originially, our motivation comes from algebraic number theory.