C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras

Brenken, Berndt

Canadian mathematical bulletin, Tome 45 (2002) no. 3, pp. 321-336

Résumé

The Cuntz-Krieger algebra ${{\mathcal{O}}_{B}}$ is defined for an arbitrary, possibly infinite and infinite valued, matrix $B$ . A graph ${{C}^{*}}$ -algebra ${{G}^{*}}\left( E \right)$ is introduced for an arbitrary directed graph $E$ , and is shown to coincide with a previously defined graph algebra ${{C}^{*}}\left( E \right)$ if each source of $E$ emits only finitely many edges. Each graph algebra ${{G}^{*}}\left( E \right)$ is isomorphic to the Cuntz-Krieger algebra ${{\mathcal{O}}_{B}}$ where $B$ is the vertex matrix of $E$ .

Détail

DOI : 10.4153/CMB-2002-035-6

Mots-clés : 46LXX, 05C50

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