Cuntz-Krieger algebras of infinite graphs and matrices

Raeburn, Iain; Szymański, Wojciech

doi:10.1090/S0002-9947-03-03341-5

Cuntz-Krieger algebras of infinite graphs and matrices
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by Iain Raeburn and Wojciech Szymański PDF

Trans. Amer. Math. Soc. 356 (2004), 39-59 Request permission

Abstract:

We show that the Cuntz-Krieger algebras of infinite graphs and infinite $\{0,1\}$-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness theorems for Cuntz-Krieger algebras and to compute their $K$-theory. Since the finite approximating graphs have sinks, we have to calculate the $K$-theory of Cuntz-Krieger algebras of graphs with sinks, and the direct methods we use to do this should be of independent interest.

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