Generalized Cuntz-Krieger algebras

Abstract

To a special embedding Φ \Phi of circle algebras having the same spectrum, we associate an r-discrete, locally compact groupoid, similar to the Cuntz-Krieger groupoid. Its C ∗ \mathbf {C}^* -algebra, denoted O Φ \mathcal {O}_{\Phi } , is a continuous version of the Cuntz-Krieger algebras O A \mathcal {O}_A . The algebra O Φ \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.