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Graph C*-algebras are singly generated

Jakub Curda, Julian Gonzales, Victor Wu

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.

Graph C*-algebras are singly generated

Abstract

We show that the -algebra of a countable directed graph is singly generated. As a consequence, any -algebra generated by a countable family of projections and partial isometries satisfying Cuntz-Krieger relations is singly generated.
Paper Structure (8 sections, 12 theorems, 37 equations)

This paper contains 8 sections, 12 theorems, 37 equations.

Table of Contents

  1. Preliminaries and basic facts - spectra
  2. Spectra
  3. Graphs with no sinks
  4. A generator for $C^*(E)$
  5. The proof
  6. Interior edges
  7. Boundary edges
  8. Sinks and sink edges

Key Result

Theorem A

Let $E$ be a countable directed graph. Then $C^*(E)$ is singly generated.

Theorems & Definitions (25)

  • Theorem A
  • Definition 1
  • Definition 2: Fowler-Laca-Raeburn
  • Lemma 5
  • proof
  • Lemma 6
  • proof
  • Lemma 7
  • proof
  • Corollary 8
  • ...and 15 more