Graph C*-algebras are singly generated

TL;DR

This paper proves that the C*-algebra associated with any countable directed graph can be generated by a single element, simplifying the understanding of its structure and implications for related algebras.

Contribution

It establishes that all countable graph C*-algebras are singly generated, extending the class of known singly generated C*-algebras and simplifying their analysis.

Findings

Countable graph C*-algebras are singly generated.

Any C*-algebra with projections and partial isometries satisfying Cuntz-Krieger relations is singly generated.

Simplifies the structural understanding of these algebras.

Abstract

We show that the $C^*$-algebra of a countable directed graph is singly generated. As a consequence, any $C^*$-algebra generated by a countable family of projections and partial isometries satisfying Cuntz-Krieger relations is singly generated.