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Journal of Operator Theory

Volume 51, Issue 1, Winter 2004  pp. 19-34.

Endomorphisms of type I von Neumann algebras with discrete center

Authors Berndt Brenken
Author institution: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada

Summary:  A version of Cuntz-Krieger algebras associated with infinite, possibly infinite valued matrices with any number of zero entries correspond to $C^{\ast}$-algebras of directed graphs with any number of edges, sources, sinks, and isolated vertices. We show that the correspondence established previously between representations and $\ast$-endomorphisms involving the original Cuntz-Krieger algebras extends to this setting, so to a correspondence between representations of Cuntz-Krieger algebras for infinite matrices and $\ast$-endomorphisms of a direct sum of type I factors.

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