On certain Cuntz-Pimsner algebras

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