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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])
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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

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