On certain Cuntz-Pimsner algebras

• Autores: Alex Kumjian
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 217, Nº 2, 2004, págs. 275-290
• Idioma: inglés
• DOI: 10.2140/pjm.2004.217.275
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• Resumen

  • 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.