Abstract

Let A be a separable unital C^*-algebra. Let π : A →L(H) be a faithful representation of A on a separable Hilbert space H such that π(A) ∩K(H) = {0}. We show that O_E, the Cuntz–Pimsner algebra associated to the Hilbert A-bimodule E = H ×_CA, is simple and purely infinite. If A is nuclear and belongs to the bootstrap class to which the UCT applies, the same applies to O_E. Hence by the Kirchberg–Phillips Theorem the isomorphism class of O_E only depends on the K-theory of A and the class of the unit.

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