On certain Cuntz–Pimsner algebras

Alex Kumjian

Vol. 217 (2004), No. 2, 275–289

DOI: 10.2140/pjm.2004.217.275

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.

Milestones

Received: 31 August 2001

Revised: 15 January 2004

Published: 1 December 2004