Journal of Operator Theory

Volume 45, Issue 1, Winter 2001 pp. 209-229.

$C^*$-equivalences of graphs

Authors: D. Drinen (1), and N. Sieben (2)
Author institution: D. Drinen (1), and N. Sieben (2)

Summary: Several relations on graphs, including primitive equivalence, explosion equivalence and strong shift equivalence, are examined and shown to preserve either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and Renault, or the groupoid of a pointed version of the graph. Thus these relations preserve either the isomorphism class or the Morita equivalence class of the graph $C^*$-algebra, as defined by Kumjian, Pask, and Raeburn.

Keywords: Graph $C^*$-algebra, graph groupoid, primitive equivalence, explosion, strong shift equivalence

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