<i>C</i><sup>*</sup>-Algebras of Infinite Graphs and Cuntz-Krieger Algebras
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Abstract
Abstract The Cuntz-Krieger algebra 𝓞 B is defined for an arbitrary, possibly infinite and infinite valued, matrix B . A graph C * -algebra G * ( E ) is introduced for an arbitrary directed graph E , and is shown to coincide with a previously defined graph algebra C * ( E ) if each source of E emits only finitely many edges. Each graph algebra G * ( E ) is isomorphic to the Cuntz-Krieger algebra 𝓞 B where B is the vertex matrix of E .
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