The ideal structure of the C*-algebras of infinite graphs

TL;DR

This paper classifies gauge-invariant ideals in C*-algebras of infinite graphs, describes their quotients, and analyzes their primitive ideals and K-theory, advancing understanding of infinite graph C*-algebras.

Contribution

It provides a comprehensive classification of gauge-invariant ideals and their quotients, and characterizes primitive ideals and K-theory for infinite graph C*-algebras.

Findings

Classification of gauge-invariant ideals in infinite graph C*-algebras

Description of quotients as graph algebras

Identification of primitive ideals and computation of K-theory

Abstract

We classify the gauge-invariant ideals in the C*-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant primitive ideals in terms of the structural properties of the graph, and describe the K-theory of the C*-algebras of arbitrary infinite graphs.