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

Abstract

AbstractThe Cuntz-Krieger algebra 𝓞B 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 𝓞B where B is the vertex matrix of E.