Resumen de On certain Cuntz-Pimsner algebras

Alex Kumjian

• Let A be a separable unital C.-algebra. Let ð : A ¿¿ L(H) be a faithful representation of A on a separable Hilbert space H such that ð(A) ¿¿ K(H) = {0}. We show that OE, the Cuntz- Pimsner algebra associated to the Hilbert A-bimodule E = H.CA, is simple and purely in.nite. If A is nuclear and belongs to the bootstrap class to which the UCT applies, the same applies to OE. Hence by the Kirchberg-Phillips Theorem the isomorphism class of OE only depends on the K-theory of A and the class of the unit.