Geodesic
C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras
Canadian mathematical bulletin, Tome 45 (2002) no. 3, pp. 321-336

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DOI

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 $E$ .
DOI : 10.4153/CMB-2002-035-6
Mots-clés : 46LXX, 05C50 
Brenken, Berndt. C *-Algebras of Infinite Graphs and Cuntz-Krieger Algebras. Canadian mathematical bulletin, Tome 45 (2002) no. 3, pp. 321-336. doi: 10.4153/CMB-2002-035-6
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     title = {C {*-Algebras} of {Infinite} {Graphs} and {Cuntz-Krieger} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {321--336},
     year = {2002},
     volume = {45},
     number = {3},
     doi = {10.4153/CMB-2002-035-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-035-6/}
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