Generalized Cuntz-Krieger algebras

Deaconu, Valentin

doi:10.1090/S0002-9939-96-03484-3

Generalized Cuntz-Krieger algebras
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Proc. Amer. Math. Soc. 124 (1996), 3427-3435 Request permission

Abstract:

To a special embedding $\Phi$ of circle algebras having the same spectrum, we associate an r-discrete, locally compact groupoid, similar to the Cuntz-Krieger groupoid. Its $\mathbf {C}^*$-algebra, denoted $\mathcal {O}_{\Phi }$, is a continuous version of the Cuntz-Krieger algebras $\mathcal {O}_A$. The algebra $\mathcal {O}_{\Phi }$ is generated by an AT-algebra and a nonunitary isometry. We compute its K-theory under the assumption that the AT-algebra is simple.

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