Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T04:45:59.779Z Has data issue: false hasContentIssue false
  • English
  • Français

Purely infinite and stable C^*-algebras of graphs and dynamical systems

Published online by Cambridge University Press:  28 November 2001

JACOB v.B. HJELMBORG
JACOB v.B. HJELMBORG
Affiliation:
Department of Mathematics and Computer Science, Odense University, Campusvej 55, DK-5230 Odense M, Denmark (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

C^*-algebras arising from directed graphs and their generalizations, Exel–Laca algebras \mathcal{O}_A of an infinite matrix A, are considered. Characterizations of pure infiniteness (in the sense of [11]) and of stability are given. In particular, these C^*-algebras admit no non-zero trace if and only if they are purely infinite. Stability is characterized by the absence of non-zero unital quotients and a bounded trace. Also, graph-theoretical analogues of pure infiniteness and stability are obtained.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 6 , December 2001 , pp. 1789 - 1808
Copyright
2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)