Let X be a Hilbert bimodule over a C*-algebra A. We analyse the structure of the associated Cuntz-Pimsner algebra OX and related algebras using representation-theoretic methods. In particular, we study the ideals I(I) in OX induced by appropriately invariant ideals I in A, and identify the quotients OX/I(I) as relative Cuntz-Pimsner algebras of Muhly and Solel. We also prove a gauge-invariant uniqueness theorem for OX, and investigate the relationship between OX and an alternative model proposed by Doplicher, Pinzari and Zuccante.
Indiana University Mathematics Journal Vol. 52, Issue 3, p. 569-605